LMFDB - Embedded newform 100.9.j.b.11.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.39
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.39

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.28596 - 13.6873i) q^{2} +(89.5931 + 29.1106i) q^{3} +(-118.686 + 226.825i) q^{4} +(-624.689 + 19.7078i) q^{5} +(-343.919 - 1467.50i) q^{6} -1003.88i q^{7} +(4088.06 - 254.974i) q^{8} +(1871.54 + 1359.75i) q^{9} +(5445.90 + 8387.03i) q^{10} +(5707.24 + 7855.34i) q^{11} +(-17236.4 + 16867.0i) q^{12} +(-31703.7 - 23034.1i) q^{13} +(-13740.4 + 8318.08i) q^{14} +(-56541.6 - 16419.4i) q^{15} +(-37363.4 - 53841.9i) q^{16} +(17422.3 + 53620.2i) q^{17} +(3103.88 - 36883.2i) q^{18} +(168174. - 54643.0i) q^{19} +(69671.5 - 144034. i) q^{20} +(29223.4 - 89940.4i) q^{21} +(60228.6 - 143206. i) q^{22} +(48326.1 + 66515.1i) q^{23} +(373684. + 96161.7i) q^{24} +(389848. - 24622.5i) q^{25} +(-52579.5 + 624799. i) q^{26} +(-235199. - 323724. i) q^{27} +(227704. + 119146. i) q^{28} +(-157167. + 483712. i) q^{29} +(243764. + 909953. i) q^{30} +(-753344. + 244776. i) q^{31} +(-427360. + 957536. i) q^{32} +(282656. + 869925. i) q^{33} +(589557. - 682759. i) q^{34} +(19784.2 + 627111. i) q^{35} +(-530551. + 263129. i) q^{36} +(3.00094e6 + 2.18031e6i) q^{37} +(-2.14140e6 - 1.84908e6i) q^{38} +(-2.16990e6 - 2.98661e6i) q^{39} +(-2.54874e6 + 239846. i) q^{40} +(2.51995e6 + 1.83085e6i) q^{41} +(-1.47319e6 + 345252. i) q^{42} +5.08373e6i q^{43} +(-2.45916e6 + 362228. i) q^{44} +(-1.19593e6 - 812539. i) q^{45} +(509986. - 1.21260e6i) q^{46} +(4.55608e6 + 1.48036e6i) q^{47} +(-1.78013e6 - 5.91153e6i) q^{48} +4.75703e6 q^{49} +(-3.56728e6 - 5.13196e6i) q^{50} +5.31117e6i q^{51} +(8.98750e6 - 4.45738e6i) q^{52} +(1.79340e6 - 5.51951e6i) q^{53} +(-2.48206e6 + 5.90161e6i) q^{54} +(-3.72006e6 - 4.79467e6i) q^{55} +(-255962. - 4.10390e6i) q^{56} +1.66579e7 q^{57} +(7.92300e6 - 1.85681e6i) q^{58} +(1.32908e6 - 1.82932e6i) q^{59} +(1.04350e7 - 1.08763e7i) q^{60} +(-1.41872e7 + 1.03076e7i) q^{61} +(9.59251e6 + 8.28306e6i) q^{62} +(1.36502e6 - 1.87879e6i) q^{63} +(1.66472e7 - 2.08469e6i) q^{64} +(2.02589e7 + 1.37643e7i) q^{65} +(9.56487e6 - 1.10770e7i) q^{66} +(2.79483e7 - 9.08096e6i) q^{67} +(-1.42302e7 - 2.41215e6i) q^{68} +(2.39339e6 + 7.36610e6i) q^{69} +(8.41954e6 - 5.46701e6i) q^{70} +(7.40334e6 + 2.40549e6i) q^{71} +(7.99766e6 + 5.08155e6i) q^{72} +(7.52022e6 - 5.46376e6i) q^{73} +(4.97696e6 - 5.91408e7i) q^{74} +(3.56445e7 + 9.14270e6i) q^{75} +(-7.56543e6 + 4.46314e7i) q^{76} +(7.88579e6 - 5.72936e6i) q^{77} +(-2.28990e7 + 5.44471e7i) q^{78} +(-2.50843e7 - 8.15037e6i) q^{79} +(2.44016e7 + 3.28981e7i) q^{80} +(-1.63387e7 - 5.02852e7i) q^{81} +(4.17924e6 - 4.96617e7i) q^{82} +(3.74353e7 - 1.21635e7i) q^{83} +(1.69323e7 + 1.73033e7i) q^{84} +(-1.19402e7 - 3.31526e7i) q^{85} +(6.95827e7 - 4.21236e7i) q^{86} +(-2.81622e7 + 3.87620e7i) q^{87} +(2.53344e7 + 3.06579e7i) q^{88} +(3.63526e7 - 2.64117e7i) q^{89} +(-1.21208e6 + 2.31017e7i) q^{90} +(-2.31234e7 + 3.18266e7i) q^{91} +(-2.08229e7 + 3.06717e6i) q^{92} -7.46200e7 q^{93} +(-1.74893e7 - 7.46267e7i) q^{94} +(-1.03979e8 + 3.74492e7i) q^{95} +(-6.61629e7 + 7.33480e7i) q^{96} +(-1.64337e7 + 5.05777e7i) q^{97} +(-3.94166e7 - 6.51111e7i) q^{98} +2.24620e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−8.28596	−	13.6873i	−0.517872	−	0.855458i
$2$	−8.28596	−	13.6873i	−0.517872	−	0.855458i
$3$	89.5931	+	29.1106i	1.10609	+	0.359390i	0.804442	−	0.594031i	$-0.202464\pi$
$3$	89.5931	+	29.1106i	1.10609	+	0.359390i	0.301645	+	0.953420i	$0.402464\pi$
$4$	−118.686	+	226.825i	−0.463616	+	0.886036i
$5$	−624.689	+	19.7078i	−0.999503	+	0.0315325i
$5$	−624.689	+	19.7078i	−0.999503	+	0.0315325i
$6$	−343.919	−	1467.50i	−0.265370	−	1.13233i
$7$		−	1003.88i		−	0.418108i	−0.977904	−	0.209054i	$-0.932962\pi$
$7$		−	1003.88i		−	0.418108i	0.977904	−	0.209054i	$-0.0670384\pi$
$8$	4088.06	−	254.974i	0.998061	−	0.0622495i
$9$	1871.54	+	1359.75i	0.285252	+	0.207248i
$10$	5445.90	+	8387.03i	0.544590	+	0.838703i
$11$	5707.24	+	7855.34i	0.389812	+	0.536530i	0.958151	−	0.286265i	$-0.0924137\pi$
$11$	5707.24	+	7855.34i	0.389812	+	0.536530i	−0.568339	+	0.822795i	$0.692414\pi$
$12$	−17236.4	+	16867.0i	−0.831233	+	0.813415i
$13$	−31703.7	−	23034.1i	−1.11004	−	0.806488i	−0.127366	−	0.991856i	$-0.540652\pi$
$13$	−31703.7	−	23034.1i	−1.11004	−	0.806488i	−0.982669	+	0.185368i	$0.940652\pi$
$14$	−13740.4	+	8318.08i	−0.357673	+	0.216526i
$15$	−56541.6	−	16419.4i	−1.11687	−	0.324333i
$16$	−37363.4	−	53841.9i	−0.570120	−	0.821562i
$17$	17422.3	+	53620.2i	0.208597	+	0.641996i	0.999546	+	0.0301145i	$0.00958719\pi$
$17$	17422.3	+	53620.2i	0.208597	+	0.641996i	−0.790949	+	0.611882i	$0.790413\pi$
$18$	3103.88	−	36883.2i	0.0295675	−	0.351349i
$19$	168174.	−	54643.0i	1.29046	−	0.419295i	0.418206	−	0.908352i	$-0.362659\pi$
$19$	168174.	−	54643.0i	1.29046	−	0.419295i	0.872252	+	0.489057i	$0.162659\pi$
$20$	69671.5	−	144034.i	0.435447	−	0.900214i
$21$	29223.4	−	89940.4i	0.150264	−	0.462464i
$22$	60228.6	−	143206.i	0.257106	−	0.611322i
$23$	48326.1	+	66515.1i	0.172691	+	0.237689i	0.886586	−	0.462564i	$-0.153070\pi$
$23$	48326.1	+	66515.1i	0.172691	+	0.237689i	−0.713895	+	0.700253i	$0.753070\pi$
$24$	373684.	+	96161.7i	1.12631	+	0.289839i
$25$	389848.	−	24622.5i	0.998011	−	0.0630335i
$26$	−52579.5	+	624799.i	−0.115060	+	1.36725i
$27$	−235199.	−	323724.i	−0.442569	−	0.609143i
$28$	227704.	+	119146.i	0.370458	+	0.193841i
$29$	−157167.	+	483712.i	−0.222214	+	0.683903i	0.776349	+	0.630303i	$0.217069\pi$
$29$	−157167.	+	483712.i	−0.222214	+	0.683903i	−0.998563	+	0.0535997i	$0.982931\pi$
$30$	243764.	+	909953.i	0.300943	+	1.12340i
$31$	−753344.	+	244776.i	−0.815730	+	0.265047i	−0.687023	−	0.726636i	$-0.741083\pi$
$31$	−753344.	+	244776.i	−0.815730	+	0.265047i	−0.128707	+	0.991683i	$0.541083\pi$
$32$	−427360.	+	957536.i	−0.407562	+	0.913178i
$33$	282656.	+	869925.i	0.238343	+	0.733544i
$34$	589557.	−	682759.i	0.441174	−	0.510918i
$35$	19784.2	+	627111.i	0.0131840	+	0.417900i
$36$	−530551.	+	263129.i	−0.315877	+	0.156660i
$37$	3.00094e6	+	2.18031e6i	1.60122	+	1.16335i	0.885129	+	0.465345i	$0.154070\pi$
$37$	3.00094e6	+	2.18031e6i	1.60122	+	1.16335i	0.716089	+	0.698009i	$0.245930\pi$
$38$	−2.14140e6	−	1.84908e6i	−1.02698	−	0.886791i
$39$	−2.16990e6	−	2.98661e6i	−0.937953	−	1.29098i
$40$	−2.54874e6	+	239846.i	−0.995601	+	0.0936898i
$41$	2.51995e6	+	1.83085e6i	0.891776	+	0.647913i	0.936341	−	0.351093i	$-0.114190\pi$
$41$	2.51995e6	+	1.83085e6i	0.891776	+	0.647913i	−0.0445643	+	0.999007i	$0.514190\pi$
$42$	−1.47319e6	+	345252.i	−0.473436	+	0.110953i
$43$			5.08373e6i			1.48699i	0.668740	+	0.743496i	$0.266834\pi$
$43$			5.08373e6i			1.48699i	−0.668740	+	0.743496i	$0.733166\pi$
$44$	−2.45916e6	+	362228.i	−0.656108	+	0.0966433i
$45$	−1.19593e6	−	812539.i	−0.291645	−	0.198150i
$46$	509986.	−	1.21260e6i	0.113901	−	0.270823i
$47$	4.55608e6	+	1.48036e6i	0.933683	+	0.303372i	0.736068	−	0.676908i	$-0.236680\pi$
$47$	4.55608e6	+	1.48036e6i	0.933683	+	0.303372i	0.197615	+	0.980280i	$0.436680\pi$
$48$	−1.78013e6	−	5.91153e6i	−0.335342	−	1.11361i
$49$	4.75703e6			0.825186
$50$	−3.56728e6	−	5.13196e6i	−0.570765	−	0.821113i
$51$			5.31117e6i			0.785072i
$52$	8.98750e6	−	4.45738e6i	1.22921	−	0.609631i
$53$	1.79340e6	−	5.51951e6i	0.227286	−	0.699515i	−0.770765	−	0.637119i	$-0.780126\pi$
$53$	1.79340e6	−	5.51951e6i	0.227286	−	0.699515i	0.998051	−	0.0623956i	$-0.0198741\pi$
$54$	−2.48206e6	+	5.90161e6i	−0.291902	+	0.694057i
$55$	−3.72006e6	−	4.79467e6i	−0.406536	−	0.523971i
$56$	−255962.	−	4.10390e6i	−0.0260270	−	0.417297i
$57$	1.66579e7			1.57805
$58$	7.92300e6	−	1.85681e6i	0.700129	−	0.164080i
$59$	1.32908e6	−	1.82932e6i	0.109684	−	0.150967i	−0.750646	−	0.660705i	$-0.770258\pi$
$59$	1.32908e6	−	1.82932e6i	0.109684	−	0.150967i	0.860330	+	0.509738i	$0.170258\pi$
$60$	1.04350e7	−	1.08763e7i	0.805170	−	0.839221i
$61$	−1.41872e7	+	1.03076e7i	−1.02465	+	0.744454i	−0.967232	−	0.253896i	$-0.918288\pi$
$61$	−1.41872e7	+	1.03076e7i	−1.02465	+	0.744454i	−0.0574216	+	0.998350i	$0.518288\pi$
$62$	9.59251e6	+	8.28306e6i	0.649181	+	0.560563i
$63$	1.36502e6	−	1.87879e6i	0.0866519	−	0.119266i
$64$	1.66472e7	−	2.08469e6i	0.992250	−	0.124257i
$65$	2.02589e7	+	1.37643e7i	1.13491	+	0.771085i
$66$	9.56487e6	−	1.10770e7i	0.504085	−	0.583774i
$67$	2.79483e7	−	9.08096e6i	1.38694	−	0.450643i	0.481993	−	0.876175i	$-0.339913\pi$
$67$	2.79483e7	−	9.08096e6i	1.38694	−	0.450643i	0.904943	+	0.425532i	$0.139913\pi$
$68$	−1.42302e7	−	2.41215e6i	−0.665541	−	0.112815i
$69$	2.39339e6	+	7.36610e6i	0.105589	+	0.324968i
$70$	8.41954e6	−	5.46701e6i	0.350668	−	0.227697i
$71$	7.40334e6	+	2.40549e6i	0.291336	+	0.0946608i	0.451039	−	0.892504i	$-0.351054\pi$
$71$	7.40334e6	+	2.40549e6i	0.291336	+	0.0946608i	−0.159703	+	0.987165i	$0.551054\pi$
$72$	7.99766e6	+	5.08155e6i	0.297600	+	0.189089i
$73$	7.52022e6	−	5.46376e6i	0.264813	−	0.192398i	−0.447453	−	0.894307i	$-0.647669\pi$
$73$	7.52022e6	−	5.46376e6i	0.264813	−	0.192398i	0.712266	+	0.701910i	$0.247669\pi$
$74$	4.97696e6	−	5.91408e7i	0.165973	−	1.97224i
$75$	3.56445e7	+	9.14270e6i	1.12654	+	0.288954i
$76$	−7.56543e6	+	4.46314e7i	−0.226767	+	1.33778i
$77$	7.88579e6	−	5.72936e6i	0.224327	−	0.162983i
$78$	−2.28990e7	+	5.44471e7i	−0.618640	+	1.47094i
$79$	−2.50843e7	−	8.15037e6i	−0.644010	−	0.209252i	−0.0312391	−	0.999512i	$-0.509945\pi$
$79$	−2.50843e7	−	8.15037e6i	−0.644010	−	0.209252i	−0.612771	+	0.790260i	$0.709945\pi$
$80$	2.44016e7	+	3.28981e7i	0.595742	+	0.803176i
$81$	−1.63387e7	−	5.02852e7i	−0.379556	−	1.16815i
$82$	4.17924e6	−	4.96617e7i	0.0924362	−	1.09841i
$83$	3.74353e7	−	1.21635e7i	0.788803	−	0.256298i	0.113209	−	0.993571i	$-0.463887\pi$
$83$	3.74353e7	−	1.21635e7i	0.788803	−	0.256298i	0.675594	+	0.737274i	$0.263887\pi$
$84$	1.69323e7	+	1.73033e7i	0.340095	+	0.347545i
$85$	−1.19402e7	−	3.31526e7i	−0.228737	−	0.635099i
$86$	6.95827e7	−	4.21236e7i	1.27206	−	0.770073i
$87$	−2.81622e7	+	3.87620e7i	−0.491575	+	0.676596i
$88$	2.53344e7	+	3.06579e7i	0.422455	+	0.511224i
$89$	3.63526e7	−	2.64117e7i	0.579397	−	0.420956i	−0.259110	−	0.965848i	$-0.583429\pi$
$89$	3.63526e7	−	2.64117e7i	0.579397	−	0.420956i	0.838507	+	0.544892i	$0.183429\pi$
$90$	−1.21208e6	+	2.31017e7i	−0.0184739	+	0.352107i
$91$	−2.31234e7	+	3.18266e7i	−0.337199	+	0.464114i
$92$	−2.08229e7	+	3.06717e6i	−0.290663	+	0.0428141i
$93$	−7.46200e7			−0.997525
$94$	−1.74893e7	−	7.46267e7i	−0.224007	−	0.955835i
$95$	−1.03979e8	+	3.74492e7i	−1.27660	+	0.459778i
$96$	−6.61629e7	+	7.33480e7i	−0.778986	+	0.863581i
$97$	−1.64337e7	+	5.05777e7i	−0.185630	+	0.571310i	−0.999959	−	0.00909375i	$-0.997105\pi$
$97$	−1.64337e7	+	5.05777e7i	−0.185630	+	0.571310i	0.814329	+	0.580404i	$0.197105\pi$
$98$	−3.94166e7	−	6.51111e7i	−0.427341	−	0.705912i
$99$			2.24620e7i			0.233834i
$100$	−4.06844e7	+	9.13497e7i	−0.406844	+	0.913497i
$101$	9.52737e7			0.915562			0.457781	−	0.889065i	$-0.348644\pi$
$101$	9.52737e7			0.915562			0.457781	+	0.889065i	$0.348644\pi$
$102$	7.26957e7	−	4.40081e7i	0.671596	−	0.406567i
$103$	−5.96443e7	−	1.93796e7i	−0.529932	−	0.172185i	0.0318159	−	0.999494i	$-0.489871\pi$
$103$	−5.96443e7	−	1.93796e7i	−0.529932	−	0.172185i	−0.561748	+	0.827308i	$0.689871\pi$
$104$	−1.35480e8	−	8.60811e7i	−1.15809	−	0.735825i
$105$	−1.64830e7	+	5.67607e7i	−0.135606	+	0.466972i
$106$	−9.04073e7	+	2.11876e7i	−0.716111	+	0.167826i
$107$			1.61542e8i			1.23239i	0.787592	+	0.616197i	$0.211328\pi$
$107$			1.61542e8i			1.23239i	−0.787592	+	0.616197i	$0.788672\pi$
$108$	1.01344e8	−	1.49277e7i	0.744905	−	0.109723i
$109$	−1.08044e8	−	7.84986e7i	−0.765411	−	0.556104i	0.135154	−	0.990825i	$-0.456847\pi$
$109$	−1.08044e8	−	7.84986e7i	−0.765411	−	0.556104i	−0.900565	+	0.434721i	$0.856847\pi$
$110$	−3.48019e7	+	9.06461e7i	−0.237702	+	0.619125i
$111$	2.05394e8	+	2.82700e8i	1.35299	+	1.86223i
$112$	−5.40506e7	+	3.75082e7i	−0.343501	+	0.238371i
$113$	6.92801e7	+	5.03349e7i	0.424908	+	0.308714i	0.779610	−	0.626266i	$-0.215418\pi$
$113$	6.92801e7	+	5.03349e7i	0.424908	+	0.308714i	−0.354702	+	0.934980i	$0.615418\pi$
$114$	−1.38027e8	−	2.28002e8i	−0.817229	−	1.34996i
$115$	−3.14996e7	−	4.05989e7i	−0.180100	−	0.232125i
$116$	−9.10645e7	−	9.30592e7i	−0.502941	−	0.513958i
$117$	−2.80141e7	−	8.62185e7i	−0.149497	−	0.460105i
$118$	−3.60511e7	−	3.03386e6i	−0.185948	−	0.0156483i
$119$	5.38280e7	−	1.74898e7i	0.268424	−	0.0872161i
$120$	−2.35332e8	−	5.27067e7i	−1.13489	−	0.254180i
$121$	3.71068e7	−	1.14203e8i	0.173106	−	0.532765i
$122$	2.58638e8	+	1.08776e8i	1.16749	+	0.491015i
$123$	1.72473e8	+	2.37388e8i	0.753529	+	1.03714i
$124$	3.38898e7	−	1.99929e8i	0.143345	−	0.845647i
$125$	−2.43049e8	+	2.30644e7i	−0.995528	+	0.0944719i
$126$	−3.70262e7	−	3.11591e6i	−0.146902	−	0.0123624i
$127$	2.68232e8	+	3.69189e8i	1.03109	+	1.41917i	0.904128	+	0.427262i	$0.140522\pi$
$127$	2.68232e8	+	3.69189e8i	1.03109	+	1.41917i	0.126959	+	0.991908i	$0.459478\pi$
$128$	−1.66472e8	−	2.10582e8i	−0.620156	−	0.784479i
$129$	−1.47990e8	+	4.55467e8i	−0.534410	+	1.64474i
$130$	2.05325e7	−	3.91341e8i	0.0718899	−	1.37019i
$131$	4.46212e7	−	1.44983e7i	0.151515	−	0.0492302i	−0.232278	−	0.972650i	$-0.574618\pi$
$131$	4.46212e7	−	1.44983e7i	0.151515	−	0.0492302i	0.383793	+	0.923419i	$0.374618\pi$
$132$	−2.30868e8	−	3.91342e7i	−0.760446	−	0.128902i
$133$	−5.48548e7	−	1.68826e8i	−0.175311	−	0.539550i
$134$	−3.55873e8	−	3.07293e8i	−1.10376	−	0.953090i
$135$	1.53306e8	+	1.97592e8i	0.461556	+	0.594885i
$136$	8.48949e7	+	2.14760e8i	0.248157	+	0.627766i
$137$	1.38804e7	+	1.00847e7i	0.0394021	+	0.0286273i	0.607312	−	0.794463i	$-0.292248\pi$
$137$	1.38804e7	+	1.00847e7i	0.0394021	+	0.0286273i	−0.567910	+	0.823091i	$0.692248\pi$
$138$	8.09906e7	−	9.37943e7i	0.223315	−	0.258619i
$139$	−2.39410e8	−	3.29520e8i	−0.641333	−	0.882719i	0.357353	−	0.933969i	$-0.383679\pi$
$139$	−2.39410e8	−	3.29520e8i	−0.641333	−	0.882719i	−0.998686	+	0.0512503i	$0.983679\pi$
$140$	−1.44593e8	−	6.99416e7i	−0.376386	−	0.182064i
$141$	3.65099e8	+	2.65260e8i	0.923707	+	0.671112i
$142$	−2.84190e7	−	1.21264e8i	−0.0698965	−	0.298248i
$143$		−	3.80504e8i		−	0.909946i
$144$	3.28459e6	−	1.51572e8i	0.00763891	−	0.352508i
$145$	8.86479e7	−	3.05267e8i	0.200538	−	0.690570i
$146$	−1.37096e8	−	5.76592e7i	−0.301727	−	0.126899i
$147$	4.26197e8	+	1.38480e8i	0.912728	+	0.296563i
$148$	−8.50719e8	+	4.21917e8i	−1.77312	+	0.879388i
$149$	3.38643e8			0.687064			0.343532	−	0.939141i	$-0.388377\pi$
$149$	3.38643e8			0.687064			0.343532	+	0.939141i	$0.388377\pi$
$150$	−1.70210e8	−	5.63634e8i	−0.336217	−	1.11335i
$151$			6.20556e8i			1.19364i	0.802375	+	0.596820i	$0.203569\pi$
$151$			6.20556e8i			1.19364i	−0.802375	+	0.596820i	$0.796431\pi$
$152$	6.73572e8	−	2.66264e8i	1.26185	−	0.498813i
$153$	−4.03038e7	+	1.24042e8i	−0.0735495	+	0.226362i
$154$	−1.43761e8	−	6.04621e7i	−0.255598	−	0.107498i
$155$	4.65782e8	−	1.67756e8i	0.806967	−	0.290637i
$156$	9.34975e8	−	1.37720e8i	1.57871	−	0.232540i
$157$	−1.05089e9			−1.72966			−0.864829	−	0.502066i	$-0.832573\pi$
$157$	−1.05089e9			−1.72966			−0.864829	+	0.502066i	$0.832573\pi$
$158$	9.62904e7	+	4.10870e8i	0.154509	+	0.659289i
$159$	3.21352e8	−	4.42303e8i	0.502797	−	0.692040i
$160$	2.48096e8	−	6.06585e8i	0.378564	−	0.925575i
$161$	6.67730e7	−	4.85134e7i	0.0993796	−	0.0722035i
$162$	−5.52889e8	+	6.40294e8i	−0.802745	+	0.929650i
$163$	−4.45868e8	+	6.13684e8i	−0.631620	+	0.869350i	−0.998134	−	0.0610626i	$-0.980551\pi$
$163$	−4.45868e8	+	6.13684e8i	−0.631620	+	0.869350i	0.366514	+	0.930412i	$0.380551\pi$
$164$	−7.14364e8	+	3.54292e8i	−0.987517	+	0.489763i
$165$	−1.93716e8	−	5.37862e8i	−0.261355	−	0.725663i
$166$	−4.76672e8	−	4.11603e8i	−0.627751	−	0.542058i
$167$	−9.50587e8	+	3.08864e8i	−1.22215	+	0.397102i	−0.847866	−	0.530211i	$-0.822113\pi$
$167$	−9.50587e8	+	3.08864e8i	−1.22215	+	0.397102i	−0.374288	+	0.927312i	$0.622113\pi$
$168$	9.65345e7	−	3.75133e8i	0.121184	−	0.470921i
$169$	2.22482e8	+	6.84728e8i	0.272739	+	0.839404i
$170$	−3.54834e8	+	4.38131e8i	−0.424844	+	0.524576i
$171$	3.89045e8	+	1.26408e8i	0.455004	+	0.147840i
$172$	−1.15312e9	−	6.03367e8i	−1.31753	−	0.689394i
$173$	1.11005e9	−	8.06496e8i	1.23924	−	0.900364i	0.241696	−	0.970352i	$-0.422296\pi$
$173$	1.11005e9	−	8.06496e8i	1.23924	−	0.900364i	0.997548	+	0.0699884i	$0.0222962\pi$
$174$	7.63899e8	+	6.42854e7i	0.833372	+	0.0701319i
$175$	−2.47179e7	−	3.91359e8i	−0.0263548	−	0.417276i
$176$	2.09704e8	−	6.00790e8i	0.218553	−	0.626141i
$177$	1.72328e8	−	1.25204e8i	0.175576	−	0.127563i
$178$	−6.62723e8	−	2.78724e8i	−0.660164	−	0.277648i
$179$	−1.93794e8	−	6.29675e7i	−0.188768	−	0.0613344i	0.213108	−	0.977029i	$-0.431642\pi$
$179$	−1.93794e8	−	6.29675e7i	−0.188768	−	0.0613344i	−0.401875	+	0.915694i	$0.631642\pi$
$180$	3.26244e8	−	1.74830e8i	0.310780	−	0.166543i
$181$	4.70011e8	+	1.44654e9i	0.437919	+	1.34778i	0.890066	+	0.455832i	$0.150658\pi$
$181$	4.70011e8	+	1.44654e9i	0.437919	+	1.34778i	−0.452147	+	0.891944i	$0.649342\pi$
$182$	6.27221e8	+	5.27833e7i	0.571656	+	0.0481073i
$183$	−1.57113e9	+	5.10492e8i	−1.40091	+	0.455182i
$184$	2.14519e8	+	2.59596e8i	0.187152	+	0.226478i
$185$	−1.91763e9	−	1.30288e9i	−1.63711	−	1.11228i
$186$	6.18298e8	+	1.02135e9i	0.516590	+	0.853340i
$187$	−3.21772e8	+	4.42881e8i	−0.263137	+	0.362176i
$188$	−8.76524e8	+	8.57736e8i	−0.701669	+	0.686629i
$189$	−3.24979e8	+	2.36111e8i	−0.254688	+	0.185041i
$190$	1.37415e9	+	1.11290e9i	1.05443	+	0.853967i
$191$	9.79271e8	−	1.34785e9i	0.735817	−	1.01276i	−0.263032	−	0.964787i	$-0.584722\pi$
$191$	9.79271e8	−	1.34785e9i	0.735817	−	1.01276i	0.998848	−	0.0479775i	$-0.0152776\pi$
$192$	1.55216e9	+	2.97835e8i	1.14217	+	0.219165i
$193$	−3.31133e8			−0.238656			−0.119328	−	0.992855i	$-0.538074\pi$
$193$	−3.31133e8			−0.238656			−0.119328	+	0.992855i	$0.538074\pi$
$194$	8.28442e8	−	1.94151e8i	0.584864	−	0.137067i
$195$	1.41437e9	+	1.82294e9i	0.978195	+	1.26076i
$196$	−5.64592e8	+	1.07902e9i	−0.382570	+	0.731145i
$197$	−8.12668e6	+	2.50113e7i	−0.00539570	+	0.0166063i	−0.953718	−	0.300702i	$-0.902779\pi$
$197$	−8.12668e6	+	2.50113e7i	−0.00539570	+	0.0166063i	0.948322	+	0.317308i	$0.102779\pi$
$198$	3.07445e8	−	1.86119e8i	0.200035	−	0.121096i
$199$			1.67210e9i			1.06623i	0.846044	+	0.533114i	$0.178978\pi$
$199$			1.67210e9i			1.06623i	−0.846044	+	0.533114i	$0.821022\pi$
$200$	1.58744e9	−	2.00059e8i	0.992152	−	0.125037i
$201$	2.76833e9			1.69603
$202$	−7.89434e8	−	1.30404e9i	−0.474144	−	0.783224i
$203$	4.85587e8	+	1.57777e8i	0.285945	+	0.0929092i
$204$	−1.20471e9	−	6.30360e8i	−0.695602	−	0.363972i
$205$	−1.61027e9	−	1.09405e9i	−0.911763	−	0.619471i
$206$	2.28955e8	+	9.76950e8i	0.127140	+	0.542505i
$207$			1.90197e8i			0.103591i
$208$	−5.56407e7	+	2.56762e9i	−0.0297262	+	1.37176i
$209$	1.38905e9	+	1.00920e9i	0.728001	+	0.528923i
$210$	9.13480e8	−	2.44709e8i	0.469701	−	0.125826i
$211$	−4.01150e8	−	5.52136e8i	−0.202385	−	0.278558i	0.695746	−	0.718288i	$-0.255074\pi$
$211$	−4.01150e8	−	5.52136e8i	−0.202385	−	0.278558i	−0.898130	+	0.439730i	$0.855074\pi$
$212$	1.03911e9	+	1.06187e9i	0.514422	+	0.525690i
$213$	5.93263e8	+	4.31031e8i	0.288223	+	0.209406i
$214$	2.21108e9	−	1.33853e9i	1.05426	−	0.638223i
$215$	−1.00189e8	−	3.17575e9i	−0.0468885	−	1.48625i
$216$	−1.04405e9	−	1.26343e9i	−0.479629	−	0.580412i
$217$	2.45725e8	+	7.56264e8i	0.110818	+	0.341063i
$218$	−1.79187e8	+	2.12927e9i	−0.0793380	+	0.942768i
$219$	8.32813e8	−	2.70597e8i	0.362052	−	0.117638i
$220$	1.52907e9	−	2.74745e8i	0.652734	−	0.117284i
$221$	6.82742e8	−	2.10127e9i	0.286212	−	0.880870i
$222$	2.16752e9	−	5.15373e9i	0.892385	−	2.12183i
$223$	1.79170e8	+	2.46606e8i	0.0724511	+	0.0997204i	0.843705	−	0.536808i	$-0.180370\pi$
$223$	1.79170e8	+	2.46606e8i	0.0724511	+	0.0997204i	−0.771254	+	0.636528i	$0.780370\pi$
$224$	9.61248e8	+	4.29016e8i	0.381806	+	0.170405i
$225$	7.63097e8	+	4.84015e8i	0.297748	+	0.188855i
$226$	1.14899e8	−	1.36533e9i	0.0440434	−	0.523365i
$227$	1.10519e8	+	1.52116e8i	0.0416229	+	0.0572890i	0.829321	−	0.558772i	$-0.188727\pi$
$227$	1.10519e8	+	1.52116e8i	0.0416229	+	0.0572890i	−0.787698	+	0.616061i	$0.788727\pi$
$228$	−1.97706e9	+	3.77843e9i	−0.731610	+	1.39821i
$229$	8.27338e8	−	2.54629e9i	0.300844	−	0.925902i	−0.680352	−	0.732886i	$-0.738173\pi$
$229$	8.27338e8	−	2.54629e9i	0.300844	−	0.925902i	0.981196	−	0.193016i	$-0.0618271\pi$
$230$	−2.94685e8	+	7.67547e8i	−0.105305	+	0.274280i
$231$	8.73297e8	−	2.83751e8i	0.306700	−	0.0996529i
$232$	−5.19176e8	+	2.01751e9i	−0.179210	+	0.696409i
$233$	2.66030e8	+	8.18756e8i	0.0902624	+	0.277799i	0.985990	−	0.166804i	$-0.0533447\pi$
$233$	2.66030e8	+	8.18756e8i	0.0902624	+	0.277799i	−0.895728	+	0.444603i	$0.853345\pi$
$234$	−9.47977e8	+	1.09784e9i	−0.316180	+	0.366164i
$235$	−2.87531e9	−	8.34974e8i	−0.942785	−	0.273780i
$236$	2.57193e8	+	5.18582e8i	0.0829107	+	0.167174i
$237$	−2.01011e9	−	1.46043e9i	−0.637129	−	0.462901i
$238$	−6.85405e8	−	5.91842e8i	−0.213619	−	0.184458i
$239$	−1.16336e9	−	1.60123e9i	−0.356553	−	0.490753i	0.592631	−	0.805474i	$-0.298089\pi$
$239$	−1.16336e9	−	1.60123e9i	−0.356553	−	0.490753i	−0.949184	+	0.314721i	$0.898089\pi$
$240$	1.22853e9	+	3.65779e9i	0.370290	+	1.10249i
$241$	4.14469e9	+	3.01130e9i	1.22864	+	0.892659i	0.996787	−	0.0800926i	$-0.0255216\pi$
$241$	4.14469e9	+	3.01130e9i	1.22864	+	0.892659i	0.231852	+	0.972751i	$0.425522\pi$
$242$	−1.87060e9	+	4.38388e8i	−0.545405	+	0.127820i
$243$		−	2.35549e9i		−	0.675548i
$244$	−6.54205e8	−	4.44138e9i	−0.184567	−	1.25302i
$245$	−2.97167e9	+	9.37506e7i	−0.824776	+	0.0260201i
$246$	1.82011e9	−	4.32768e9i	0.497001	−	1.18172i
$247$	−6.59039e9	−	2.14135e9i	−1.77061	−	0.575306i
$248$	−3.01730e9	+	1.19274e9i	−0.797649	+	0.315312i
$249$	3.70803e9			0.964596
$250$	2.32958e9	+	3.13558e9i	0.596373	+	0.802707i
$251$		−	4.44916e9i		−	1.12094i	−0.828174	−	0.560470i	$-0.810620\pi$
$251$		−	4.44916e9i		−	1.12094i	0.828174	−	0.560470i	$-0.189380\pi$
$252$	2.64149e8	+	5.32608e8i	0.0655008	+	0.132070i
$253$	−2.46690e8	+	7.59235e8i	−0.0602102	+	0.185308i
$254$	2.83066e9	−	6.73046e9i	0.680068	−	1.61700i
$255$	−1.04671e8	−	3.31783e9i	−0.0247552	−	0.784682i
$256$	−1.50292e9	+	4.02343e9i	−0.349927	+	0.936777i
$257$	−7.19531e9			−1.64937			−0.824683	−	0.565595i	$-0.808647\pi$
$257$	−7.19531e9			−1.64937			−0.824683	+	0.565595i	$0.808647\pi$
$258$	7.46037e9	−	1.74839e9i	1.68377	−	0.394603i
$259$	2.18876e9	−	3.01257e9i	0.486407	−	0.669482i
$260$	−5.52655e9	+	2.96160e9i	−1.20937	+	0.648087i
$261$	−9.51873e8	+	6.91576e8i	−0.205124	+	0.149032i
$262$	−5.68172e8	−	4.90612e8i	−0.120580	−	0.104120i
$263$	3.83074e8	−	5.27257e8i	0.0800682	−	0.110204i	−0.767104	−	0.641523i	$-0.778303\pi$
$263$	3.83074e8	−	5.27257e8i	0.0800682	−	0.110204i	0.847172	+	0.531318i	$0.178303\pi$
$264$	1.37732e9	+	3.48423e9i	0.283543	+	0.717284i
$265$	−1.01154e9	+	3.48332e9i	−0.205116	+	0.706334i
$266$	−1.85625e9	+	2.14970e9i	−0.370774	+	0.429389i
$267$	4.02581e9	−	1.30806e9i	0.792151	−	0.257385i
$268$	−1.25728e9	+	7.41717e9i	−0.243720	+	1.43780i
$269$	2.10331e9	+	6.47333e9i	0.401693	+	1.23628i	0.923625	+	0.383297i	$0.125211\pi$
$269$	2.10331e9	+	6.47333e9i	0.401693	+	1.23628i	−0.521932	+	0.852987i	$0.674789\pi$
$270$	1.43421e9	−	3.73559e9i	0.269872	−	0.702917i
$271$	−5.09936e9	−	1.65688e9i	−0.945450	−	0.307195i	−0.204585	−	0.978849i	$-0.565584\pi$
$271$	−5.09936e9	−	1.65688e9i	−0.945450	−	0.307195i	−0.740865	+	0.671654i	$0.765584\pi$
$272$	2.23606e9	−	2.94148e9i	0.408514	−	0.537390i
$273$	−2.99819e9	+	2.17831e9i	−0.539769	+	0.392165i
$274$	2.30201e7	−	2.73546e8i	0.00408418	−	0.0485321i
$275$	2.41837e9	+	2.92186e9i	0.422856	+	0.510892i
$276$	−1.95488e9	−	3.31370e8i	−0.336886	−	0.0571053i
$277$	4.00657e9	−	2.91094e9i	0.680540	−	0.494441i	−0.192997	−	0.981199i	$-0.561821\pi$
$277$	4.00657e9	−	2.91094e9i	0.680540	−	0.494441i	0.873537	+	0.486758i	$0.161821\pi$
$278$	−2.52650e9	+	6.00728e9i	−0.423000	+	1.00577i
$279$	−1.74275e9	−	5.66253e8i	−0.287619	−	0.0934532i
$280$	2.40776e8	+	2.55862e9i	0.0391724	+	0.416269i
$281$	5.37211e8	+	1.65336e9i	0.0861627	+	0.265182i	0.984850	−	0.173408i	$-0.0554781\pi$
$281$	5.37211e8	+	1.65336e9i	0.0861627	+	0.265182i	−0.898687	+	0.438590i	$0.855478\pi$
$282$	6.05504e8	−	7.19516e9i	0.0957460	−	1.13774i
$283$	−8.47409e8	+	2.75340e8i	−0.132114	+	0.0429263i	−0.374327	−	0.927297i	$-0.622126\pi$
$283$	−8.47409e8	+	2.75340e8i	−0.132114	+	0.0429263i	0.242214	+	0.970223i	$0.422126\pi$
$284$	−1.42430e9	+	1.39377e9i	−0.218941	+	0.214248i
$285$	−1.04060e10	+	3.28290e8i	−1.57727	+	0.0497598i
$286$	−5.20809e9	+	3.15284e9i	−0.778420	+	0.471236i
$287$	1.83795e9	−	2.52971e9i	0.270898	−	0.372858i
$288$	−2.10183e9	+	1.21096e9i	−0.305512	+	0.176020i
$289$	3.07192e9	−	2.23188e9i	0.440371	−	0.319948i
$290$	−4.91282e9	+	1.31608e9i	−0.694607	+	0.186075i
$291$	−2.94469e9	+	4.05302e9i	−0.410646	+	0.565206i
$292$	3.46775e8	+	2.35425e9i	0.0476998	+	0.323832i
$293$	9.59899e8			0.130243			0.0651216	−	0.997877i	$-0.479256\pi$
$293$	9.59899e8			0.130243			0.0651216	+	0.997877i	$0.479256\pi$
$294$	−1.63603e9	−	6.98094e9i	−0.218979	−	0.934382i
$295$	−7.94208e8	+	1.16895e9i	−0.104869	+	0.154350i
$296$	1.28239e10	+	8.14808e9i	1.67053	+	1.06142i
$297$	1.20062e9	−	3.69514e9i	0.154305	−	0.474903i
$298$	−2.80598e9	−	4.63512e9i	−0.355811	−	0.587754i
$299$		−	3.22193e9i		−	0.403117i
$300$	−6.30429e9	+	6.99996e9i	−0.778307	+	0.864193i
$301$	5.10344e9			0.621723
$302$	8.49376e9	−	5.14190e9i	1.02111	−	0.618153i
$303$	8.53587e9	+	2.77347e9i	1.01269	+	0.329043i
$304$	−9.22562e9	−	7.01314e9i	−1.08019	−	0.821142i
$305$	8.65944e9	−	6.71864e9i	1.00067	−	0.776394i
$306$	2.03176e9	−	4.76158e8i	0.231733	−	0.0543082i
$307$			4.42477e9i			0.498124i	0.968488	+	0.249062i	$0.0801222\pi$
$307$			4.42477e9i			0.498124i	−0.968488	+	0.249062i	$0.919878\pi$
$308$	3.63633e8	+	2.46869e9i	0.0404073	+	0.274324i
$309$	−4.77957e9	−	3.47256e9i	−0.524270	−	0.380904i
$310$	−6.15558e9	−	4.98529e9i	−0.666534	−	0.539814i
$311$	−4.43203e9	−	6.10017e9i	−0.473763	−	0.652079i	0.503528	−	0.863979i	$-0.332035\pi$
$311$	−4.43203e9	−	6.10017e9i	−0.473763	−	0.652079i	−0.977291	+	0.211900i	$0.932035\pi$
$312$	−9.63218e9	−	1.16562e10i	−1.01650	−	1.23009i
$313$	−1.35424e10	−	9.83916e9i	−1.41098	−	1.02513i	−0.993180	−	0.116593i	$-0.962803\pi$
$313$	−1.35424e10	−	9.83916e9i	−1.41098	−	1.02513i	−0.417796	−	0.908541i	$-0.637197\pi$
$314$	8.70767e9	+	1.43839e10i	0.895742	+	1.47965i
$315$	−8.15689e8	+	1.20056e9i	−0.0828480	+	0.121939i
$316$	4.82585e9	−	4.72241e9i	0.483978	−	0.473604i
$317$	−3.82478e8	−	1.17715e9i	−0.0378765	−	0.116572i	0.930331	−	0.366722i	$-0.119520\pi$
$317$	−3.82478e8	−	1.17715e9i	−0.0378765	−	0.116572i	−0.968207	+	0.250150i	$0.919520\pi$
$318$	−8.71665e9	−	7.33544e8i	−0.852396	−	0.0717328i
$319$	−4.69671e9	+	1.52605e9i	−0.453556	+	0.147369i
$320$	−1.03582e10	+	1.63037e9i	−0.987838	+	0.155484i
$321$	−4.70257e9	+	1.44730e10i	−0.442910	+	1.36314i
$322$	−1.21730e9	−	5.11963e8i	−0.113233	−	0.0476228i
$323$	5.85993e9	+	8.06551e9i	0.538372	+	0.741006i
$324$	1.33451e10	+	2.26212e9i	1.21100	+	0.205275i
$325$	−1.29268e10	−	8.19918e9i	−1.15866	−	0.734915i
$326$	1.20941e10	+	1.01777e9i	1.07079	+	0.0901117i
$327$	−7.39486e9	−	1.01782e10i	−0.646754	−	0.890181i
$328$	1.07685e10	+	6.84209e9i	0.930379	+	0.591144i
$329$	1.48610e9	−	4.57374e9i	0.126842	−	0.390380i
$330$	−5.75677e9	+	7.10816e9i	−0.485426	+	0.599379i
$331$	−7.93604e9	+	2.57858e9i	−0.661138	+	0.214817i	−0.620319	−	0.784350i	$-0.712997\pi$
$331$	−7.93604e9	+	2.57858e9i	−0.661138	+	0.214817i	−0.0408189	+	0.999167i	$0.512997\pi$
$332$	−1.68405e9	+	9.93489e9i	−0.138613	+	0.817732i
$333$	2.65170e9	+	8.16108e9i	0.215649	+	0.663698i
$334$	1.21041e10	+	1.04518e10i	0.972624	+	0.839853i
$335$	−1.72801e10	+	6.22358e9i	−1.37204	+	0.494153i
$336$	−5.93444e9	+	1.78703e9i	−0.465611	+	0.140209i
$337$	−1.13030e10	−	8.21210e9i	−0.876342	−	0.636700i	0.0559389	−	0.998434i	$-0.482185\pi$
$337$	−1.13030e10	−	8.21210e9i	−0.876342	−	0.636700i	−0.932281	+	0.361734i	$0.882185\pi$
$338$	7.52862e9	−	8.71880e9i	0.576831	−	0.668021i
$339$	4.74174e9	+	6.52645e9i	0.359037	+	0.494172i
$340$	8.93698e9	+	1.22640e9i	0.668767	+	0.0917730i
$341$	−6.22231e9	−	4.52078e9i	−0.460187	−	0.334345i
$342$	−1.49342e9	−	6.37240e9i	−0.109163	−	0.465799i
$343$		−	1.05626e10i		−	0.763124i
$344$	1.29622e9	+	2.07826e10i	0.0925645	+	1.48411i
$345$	−1.64029e9	−	4.55435e9i	−0.115783	−	0.321477i
$346$	−2.02366e10	−	8.51098e9i	−1.41199	−	0.593848i
$347$	2.20934e10	+	7.17857e9i	1.52386	+	0.495131i	0.946868	−	0.321622i	$-0.104228\pi$
$347$	2.20934e10	+	7.17857e9i	1.52386	+	0.495131i	0.576988	+	0.816753i	$0.304228\pi$
$348$	−5.44974e9	−	1.09884e10i	−0.371586	−	0.749234i
$349$	6.66195e9			0.449055			0.224528	−	0.974468i	$-0.427916\pi$
$349$	6.66195e9			0.449055			0.224528	+	0.974468i	$0.427916\pi$
$350$	−5.15185e9	+	3.58111e9i	−0.343314	+	0.238641i
$351$			1.56809e10i			1.03310i
$352$	−9.96081e9	+	2.10783e9i	−0.648820	+	0.137298i
$353$	−6.71286e9	+	2.06601e10i	−0.432324	+	1.33056i	0.463481	+	0.886107i	$0.346600\pi$
$353$	−6.71286e9	+	2.06601e10i	−0.432324	+	1.33056i	−0.895804	+	0.444448i	$0.853400\pi$
$354$	−3.14161e9	−	1.32128e9i	−0.200051	−	0.0841361i
$355$	−4.67219e9	−	1.35678e9i	−0.294176	−	0.0854272i
$356$	1.67631e9	+	1.13804e10i	0.104365	+	0.708529i
$357$	5.33176e9			0.328245
$358$	7.43912e8	+	3.17427e9i	0.0452887	+	0.193246i
$359$	1.18619e10	−	1.63265e10i	0.714127	−	0.982911i	−0.285572	−	0.958357i	$-0.592183\pi$
$359$	1.18619e10	−	1.63265e10i	0.714127	−	0.982911i	0.999699	−	0.0245538i	$-0.00781652\pi$
$360$	−5.09620e9	−	3.01678e9i	−0.303414	−	0.179611i
$361$	1.15566e10	−	8.39635e9i	0.680457	−	0.494381i
$362$	1.59048e10	−	1.84192e10i	0.926179	−	1.07260i
$363$	6.64902e9	−	9.15159e9i	0.382940	−	0.527072i
$364$	−4.47466e9	−	9.02234e9i	−0.254891	−	0.513941i
$365$	−4.59012e9	+	3.56136e9i	−0.258614	+	0.200652i
$366$	2.00056e10	+	1.72747e10i	1.11488	+	0.962689i
$367$	−1.23852e10	+	4.02421e9i	−0.682716	+	0.221828i	−0.629784	−	0.776770i	$-0.716857\pi$
$367$	−1.23852e10	+	4.02421e9i	−0.682716	+	0.221828i	−0.0529317	+	0.998598i	$0.516857\pi$
$368$	1.77567e9	−	5.08720e9i	0.0968215	−	0.277388i
$369$	2.22668e9	+	6.85301e9i	0.120102	+	0.369637i
$370$	−1.94352e9	+	3.70427e10i	−0.103701	+	1.97650i
$371$	−5.54090e9	−	1.80035e9i	−0.292472	−	0.0950300i
$372$	8.85633e9	−	1.69257e10i	0.462469	−	0.883843i
$373$	1.08155e10	−	7.85791e9i	0.558741	−	0.405949i	−0.272257	−	0.962225i	$-0.587770\pi$
$373$	1.08155e10	−	7.85791e9i	0.558741	−	0.405949i	0.830998	+	0.556276i	$0.187770\pi$
$374$	8.72804e9	+	7.34502e8i	0.446098	+	0.0375411i
$375$	−2.24469e10	−	5.00887e9i	−1.13509	−	0.253288i
$376$	1.90030e10	+	4.89011e9i	0.950757	+	0.244662i
$377$	1.61247e10	−	1.17152e10i	0.798225	−	0.579944i
$378$	5.92449e9	+	2.49168e9i	0.290191	+	0.122047i
$379$	1.73162e10	+	5.62636e9i	0.839256	+	0.272691i	0.696939	−	0.717130i	$-0.254545\pi$
$379$	1.73162e10	+	5.62636e9i	0.839256	+	0.272691i	0.142317	+	0.989821i	$0.454545\pi$
$380$	3.84646e9	−	2.80299e10i	0.184470	−	1.34427i
$381$	1.32844e10	+	4.08852e10i	0.630438	+	1.94029i
$382$	−2.65627e10	−	2.23536e9i	−1.24744	−	0.104977i
$383$	3.09369e10	−	1.00520e10i	1.43774	−	0.467151i	0.516550	−	0.856257i	$-0.327216\pi$
$383$	3.09369e10	−	1.00520e10i	1.43774	−	0.467151i	0.921193	+	0.389106i	$0.127216\pi$
$384$	−8.78457e9	−	2.37128e10i	−0.404013	−	1.09058i
$385$	−4.81325e9	+	3.73448e9i	−0.219076	+	0.169976i
$386$	2.74375e9	+	4.53232e9i	0.123594	+	0.204160i
$387$	−6.91262e9	+	9.51441e9i	−0.308176	+	0.424168i
$388$	−9.52185e9	−	9.73043e9i	−0.420140	−	0.429344i
$389$	3.29299e10	−	2.39250e10i	1.43811	−	1.04485i	0.449676	−	0.893192i	$-0.351539\pi$
$389$	3.29299e10	−	2.39250e10i	1.43811	−	1.04485i	0.988433	−	0.151656i	$-0.0484605\pi$
$390$	1.32317e10	−	3.44638e10i	0.571950	−	1.48972i
$391$	−2.72460e9	+	3.75010e9i	−0.116573	+	0.160448i
$392$	1.94470e10	−	1.21292e9i	0.823586	−	0.0513674i
$393$	4.41980e9			0.185282
$394$	4.09676e8	−	9.60105e7i	0.0170002	−	0.00398413i
$395$	1.58305e10	+	4.59709e9i	0.650288	+	0.188840i
$396$	−5.09495e9	−	2.66592e9i	−0.207185	−	0.108409i
$397$	3.31320e9	−	1.01970e10i	0.133378	−	0.410496i	−0.861956	−	0.506983i	$-0.830761\pi$
$397$	3.31320e9	−	1.01970e10i	0.133378	−	0.410496i	0.995334	+	0.0964868i	$0.0307606\pi$
$398$	2.28866e10	−	1.38550e10i	0.912113	−	0.552170i
$399$		−	1.67225e10i		−	0.659795i
$400$	−1.58918e10	−	2.00702e10i	−0.620772	−	0.783991i
$401$	7.60740e9			0.294211			0.147105	−	0.989121i	$-0.453004\pi$
$401$	7.60740e9			0.294211			0.147105	+	0.989121i	$0.453004\pi$
$402$	−2.29383e10	−	3.78910e10i	−0.878327	−	1.45088i
$403$	2.95220e10	+	9.59229e9i	1.11925	+	0.363665i
$404$	−1.13076e10	+	2.16105e10i	−0.424469	+	0.811221i
$405$	1.11976e10	+	3.10906e10i	0.416203	+	1.15561i
$406$	−1.86401e9	−	7.95371e9i	−0.0686032	−	0.292729i
$407$			3.60170e10i			1.31259i
$408$	1.35421e9	+	2.17124e10i	0.0488703	+	0.783549i
$409$	−2.23996e10	−	1.62743e10i	−0.800474	−	0.581579i	0.110579	−	0.993867i	$-0.464730\pi$
$409$	−2.23996e10	−	1.62743e10i	−0.800474	−	0.581579i	−0.911053	+	0.412289i	$0.864730\pi$
$410$	−1.63201e9	+	3.11055e10i	−0.0577546	+	1.10078i
$411$	9.50015e8	+	1.30758e9i	0.0332938	+	0.0458250i
$412$	1.14747e10	−	1.12288e10i	0.398248	−	0.389711i
$413$	−1.83641e9	−	1.33423e9i	−0.0631203	−	0.0458596i
$414$	2.60329e9	−	1.57597e9i	0.0886179	−	0.0536470i
$415$	−2.31457e10	+	8.33614e9i	−0.780329	+	0.281043i
$416$	3.56049e10	−	2.05136e10i	1.18887	−	0.684966i
$417$	−1.18570e10	−	3.64921e10i	−0.392130	−	1.20685i
$418$	2.30369e9	−	2.73745e10i	0.0754602	−	0.896689i
$419$	−1.03758e10	+	3.37129e9i	−0.336639	+	0.109381i	−0.472458	−	0.881353i	$-0.656633\pi$
$419$	−1.03758e10	+	3.37129e9i	−0.336639	+	0.109381i	0.135819	+	0.990734i	$0.456633\pi$
$420$	−1.09185e10	−	1.04755e10i	−0.350885	−	0.336648i
$421$	−4.15191e8	+	1.27783e9i	−0.0132166	+	0.0406764i	−0.957447	−	0.288608i	$-0.906808\pi$
$421$	−4.15191e8	+	1.27783e9i	−0.0132166	+	0.0406764i	0.944231	+	0.329285i	$0.106808\pi$
$422$	−4.23335e9	+	1.00657e10i	−0.133486	+	0.317389i
$423$	6.51395e9	+	8.96569e9i	0.203462	+	0.280041i
$424$	5.92418e9	−	2.30213e10i	0.183301	−	0.712307i
$425$	8.11229e9	+	2.04747e10i	0.248650	+	0.627571i
$426$	9.83906e8	−	1.16917e10i	0.0298755	−	0.355008i
$427$	1.03475e10	+	1.42422e10i	0.311262	+	0.428415i
$428$	−3.66418e10	−	1.91727e10i	−1.09195	−	0.571358i
$429$	1.10767e10	−	3.40906e10i	0.327025	−	1.00648i
$430$	−4.26374e10	+	2.76855e10i	−1.24714	+	0.809801i
$431$	2.29339e10	−	7.45168e9i	0.664614	−	0.215946i	0.0427669	−	0.999085i	$-0.486383\pi$
$431$	2.29339e10	−	7.45168e9i	0.664614	−	0.215946i	0.621847	+	0.783139i	$0.286383\pi$
$432$	−8.64206e9	+	2.47590e10i	−0.248132	+	0.710882i
$433$	1.92146e10	+	5.91365e10i	0.546613	+	1.68230i	0.717124	+	0.696946i	$0.245458\pi$
$433$	1.92146e10	+	5.91365e10i	0.546613	+	1.68230i	−0.170511	+	0.985356i	$0.554542\pi$
$434$	8.31517e9	−	9.62970e9i	0.234375	−	0.271427i
$435$	1.68287e10	−	2.47692e10i	0.469996	−	0.691760i
$436$	3.06288e10	−	1.51905e10i	0.847585	−	0.420363i
$437$	1.17618e10	+	8.54542e9i	0.322513	+	0.234319i
$438$	−1.06044e10	−	9.15682e9i	−0.288131	−	0.248799i
$439$	3.93167e10	+	5.41148e10i	1.05857	+	1.45699i	0.881137	+	0.472861i	$0.156779\pi$
$439$	3.93167e10	+	5.41148e10i	1.05857	+	1.45699i	0.177431	+	0.984133i	$0.443221\pi$
$440$	−1.64303e10	−	1.86523e10i	−0.438365	−	0.497649i
$441$	8.90297e9	+	6.46839e9i	0.235386	+	0.171018i
$442$	−3.44179e10	+	8.06608e9i	−0.901768	+	0.211336i
$443$			6.38592e10i			1.65809i	0.559180	+	0.829046i	$0.311116\pi$
$443$			6.38592e10i			1.65809i	−0.559180	+	0.829046i	$0.688884\pi$
$444$	−8.85008e10	+	1.30360e10i	−2.27727	+	0.335438i
$445$	−2.21886e10	+	1.72156e10i	−0.565835	+	0.439017i
$446$	1.89078e9	−	4.49572e9i	0.0477861	−	0.113621i
$447$	3.03401e10	+	9.85809e9i	0.759953	+	0.246924i
$448$	−2.09278e9	−	1.67117e10i	−0.0519530	−	0.414867i
$449$	3.49473e10			0.859860			0.429930	−	0.902862i	$-0.358538\pi$
$449$	3.49473e10			0.859860			0.429930	+	0.902862i	$0.358538\pi$
$450$	3.01887e8	−	1.44553e10i	0.00736197	−	0.352514i
$451$			3.02441e10i			0.731029i
$452$	−1.96398e10	+	9.74044e9i	−0.470526	+	0.233359i
$453$	−1.80647e10	+	5.55976e10i	−0.428982	+	1.32027i
$454$	1.16631e9	−	2.77313e9i	0.0274530	−	0.0652751i
$455$	1.38177e10	−	2.03375e10i	0.322396	−	0.474516i
$456$	6.80984e10	−	4.24733e9i	1.57499	−	0.0982328i
$457$	3.70953e10			0.850461			0.425231	−	0.905085i	$-0.360193\pi$
$457$	3.70953e10			0.850461			0.425231	+	0.905085i	$0.360193\pi$
$458$	−4.17071e10	+	9.77437e9i	−0.947869	+	0.222140i
$459$	1.32604e10	−	1.82514e10i	0.298749	−	0.411193i
$460$	1.29474e10	−	2.32640e9i	0.289169	−	0.0519582i
$461$	−1.55537e10	+	1.13004e10i	−0.344373	+	0.250202i	−0.746505	−	0.665380i	$-0.768269\pi$
$461$	−1.55537e10	+	1.13004e10i	−0.344373	+	0.250202i	0.402132	+	0.915582i	$0.368269\pi$
$462$	−1.11199e10	−	9.60195e9i	−0.244080	−	0.210762i
$463$	−4.39226e10	+	6.04543e10i	−0.955794	+	1.31554i	−0.00688863	+	0.999976i	$0.502193\pi$
$463$	−4.39226e10	+	6.04543e10i	−0.955794	+	1.31554i	−0.948905	+	0.315561i	$0.897807\pi$
$464$	3.19162e10	−	9.61091e9i	0.688557	−	0.207345i
$465$	4.66143e10	−	1.47060e9i	0.997029	−	0.0314544i
$466$	9.00227e9	−	1.04254e10i	0.190901	−	0.221080i
$467$	−7.39534e10	+	2.40289e10i	−1.55486	+	0.505204i	−0.955428	−	0.295224i	$-0.904606\pi$
$467$	−7.39534e10	+	2.40289e10i	−1.55486	+	0.505204i	−0.599429	+	0.800428i	$0.704606\pi$
$468$	2.28814e10	+	3.87860e9i	0.476979	+	0.0808523i
$469$	−9.11616e9	−	2.80567e10i	−0.188417	−	0.579889i
$470$	1.23961e10	+	4.62738e10i	0.254035	+	0.948296i
$471$	−9.41529e10	−	3.05921e10i	−1.91315	−	0.621621i
$472$	4.96691e9	−	7.81723e9i	0.100073	−	0.157502i
$473$	−3.99344e10	+	2.90141e10i	−0.797816	+	0.579647i
$474$	−3.33371e9	+	3.96142e10i	−0.0660410	+	0.784761i
$475$	6.42168e10	−	2.54433e10i	1.26146	−	0.499804i
$476$	−2.42150e9	+	1.42853e10i	−0.0471689	+	0.278268i
$477$	1.08616e10	−	7.89140e9i	0.209807	−	0.152434i
$478$	−1.22770e10	+	2.91911e10i	−0.235170	+	0.559163i
$479$	−9.57533e10	−	3.11121e10i	−1.81891	−	0.591001i	−0.999850	−	0.0172960i	$-0.994494\pi$
$479$	−9.57533e10	−	3.11121e10i	−1.81891	−	0.591001i	−0.819062	−	0.573705i	$-0.805506\pi$
$480$	3.98857e10	−	4.71236e10i	0.751368	−	0.887715i
$481$	−4.49195e10	−	1.38248e11i	−0.839179	−	2.58273i
$482$	6.87383e9	−	8.16813e10i	0.127353	−	1.51333i
$483$	7.39465e9	−	2.40267e9i	0.135872	−	0.0441474i
$484$	2.15001e10	+	2.19710e10i	0.391794	+	0.400377i
$485$	9.26917e9	−	3.19192e10i	0.167523	−	0.576879i
$486$	−3.22403e10	+	1.95175e10i	−0.577902	+	0.349847i
$487$	3.48331e9	−	4.79436e9i	0.0619264	−	0.0852344i	−0.776931	−	0.629586i	$-0.783224\pi$
$487$	3.48331e9	−	4.79436e9i	0.0619264	−	0.0852344i	0.838857	+	0.544352i	$0.183224\pi$
$488$	−5.53698e10	+	4.57554e10i	−0.976324	+	0.806794i
$489$	−5.78114e10	+	4.20024e10i	−1.01106	+	0.734580i
$490$	2.59063e10	+	3.98974e10i	0.449388	+	0.692086i
$491$	−3.95001e9	+	5.43673e9i	−0.0679630	+	0.0935431i	−0.841645	−	0.540031i	$-0.818413\pi$
$491$	−3.95001e9	+	5.43673e9i	−0.0679630	+	0.0935431i	0.773682	+	0.633574i	$0.218413\pi$
$492$	−7.43158e10	+	1.09466e10i	−1.26830	+	0.186817i
$493$	−2.86749e10			−0.485416
$494$	2.52984e10	+	1.07948e11i	0.424800	+	1.81262i
$495$	−4.42676e8	−	1.40318e10i	−0.00737336	−	0.233718i
$496$	4.13267e10	+	3.14158e10i	0.682816	+	0.519064i
$497$	2.41481e9	−	7.43203e9i	0.0395784	−	0.121810i
$498$	−3.07246e10	−	5.07530e10i	−0.499538	−	0.825171i
$499$		−	6.45355e10i		−	1.04087i	−0.853901	−	0.520435i	$-0.825770\pi$
$499$		−	6.45355e10i		−	1.04087i	0.853901	−	0.520435i	$-0.174230\pi$
$500$	2.36148e10	−	5.78670e10i	0.377837	−	0.925872i
$501$	−9.41573e10			−1.49452
$502$	−6.08970e10	+	3.68655e10i	−0.958918	+	0.580504i
$503$	1.14209e10	+	3.71088e9i	0.178414	+	0.0579703i	0.396862	−	0.917878i	$-0.370099\pi$
$503$	1.14209e10	+	3.71088e9i	0.178414	+	0.0579703i	−0.218448	+	0.975849i	$0.570099\pi$
$504$	5.10125e9	−	8.02866e9i	0.0790596	−	0.124429i
$505$	−5.95165e10	+	1.87763e9i	−0.915106	+	0.0288699i
$506$	1.24360e10	−	2.91446e9i	0.189704	−	0.0444586i
$507$			6.78235e10i			1.02647i
$508$	−1.15577e11	+	1.70242e10i	−1.73546	+	0.255630i
$509$	−3.99727e10	−	2.90418e10i	−0.595514	−	0.432666i	0.248770	−	0.968563i	$-0.419974\pi$
$509$	−3.99727e10	−	2.90418e10i	−0.595514	−	0.432666i	−0.844284	+	0.535896i	$0.819974\pi$
$510$	−4.45449e10	+	2.89241e10i	−0.658442	+	0.427542i
$511$	−5.48494e9	−	7.54937e9i	−0.0804430	−	0.110720i
$512$	6.75231e10	−	1.27669e10i	0.982591	−	0.185784i
$513$	−5.72436e10	−	4.15899e10i	−0.826527	−	0.600507i
$514$	5.96201e10	+	9.84846e10i	0.854162	+	1.41096i
$515$	3.76411e10	+	1.09308e10i	0.535098	+	0.155390i
$516$	−8.57472e10	−	8.76254e10i	−1.20954	−	1.23604i
$517$	1.43739e10	+	4.42383e10i	0.201193	+	0.619207i
$518$	−5.93701e10	−	4.99625e9i	−0.824610	−	0.0693945i
$519$	1.22930e11	−	3.99424e10i	1.69429	−	0.550510i
$520$	8.63292e10	+	5.11039e10i	1.18071	+	0.698942i
$521$	−1.85368e10	+	5.70505e10i	−0.251585	+	0.774299i	0.742898	+	0.669404i	$0.233451\pi$
$521$	−1.85368e10	+	5.70505e10i	−0.251585	+	0.774299i	−0.994483	+	0.104895i	$0.966549\pi$
$522$	1.73530e10	+	7.29823e9i	0.233718	+	0.0982959i
$523$	−3.75049e10	−	5.16210e10i	−0.501281	−	0.689953i	0.481138	−	0.876645i	$-0.340224\pi$
$523$	−3.75049e10	−	5.16210e10i	−0.501281	−	0.689953i	−0.982419	+	0.186691i	$0.940224\pi$
$524$	−2.00732e9	+	1.18419e10i	−0.0266251	+	0.157072i
$525$	9.17814e9	−	3.57827e10i	0.120814	−	0.471016i
$526$	−1.03909e10	−	8.74437e8i	−0.135740	−	0.0114231i
$527$	−2.62499e10	−	3.61299e10i	−0.340318	−	0.468408i
$528$	3.62774e10	−	4.77220e10i	0.466767	−	0.614021i
$529$	2.21106e10	−	6.80493e10i	0.282343	−	0.868963i
$530$	5.60589e10	−	1.50174e10i	0.710463	−	0.190323i
$531$	4.97484e9	−	1.61642e9i	0.0625750	−	0.0203318i
$532$	4.48044e10	+	7.59476e9i	0.559338	+	0.0948129i
$533$	−3.77197e10	−	1.16089e11i	−0.467369	−	1.43841i
$534$	−5.12616e10	−	4.42640e10i	−0.630415	−	0.544359i
$535$	−3.18363e9	−	1.00913e11i	−0.0388604	−	1.23178i
$536$	1.11939e11	−	4.42496e10i	1.35619	−	0.536105i
$537$	−1.55296e10	−	1.12829e10i	−0.186751	−	0.135682i
$538$	7.11746e10	−	8.24264e10i	0.849563	−	0.983869i
$539$	2.71495e10	+	3.73681e10i	0.321667	+	0.442737i
$540$	−6.30140e10	+	1.13224e10i	−0.741075	+	0.133157i
$541$	1.92757e10	+	1.40046e10i	0.225020	+	0.163486i	0.694583	−	0.719412i	$-0.255589\pi$
$541$	1.92757e10	+	1.40046e10i	0.225020	+	0.163486i	−0.469564	+	0.882899i	$0.655589\pi$
$542$	1.95748e10	+	8.35255e10i	0.226830	+	0.967881i
$543$			1.43283e11i			1.64814i
$544$	−5.87888e10	−	6.23266e9i	−0.671273	−	0.0711669i
$545$	6.90410e10	+	4.69079e10i	0.782566	+	0.531692i
$546$	5.46581e10	+	2.29878e10i	0.615013	+	0.258658i
$547$	9.13061e9	+	2.96671e9i	0.101988	+	0.0331380i	0.359567	−	0.933119i	$-0.382925\pi$
$547$	9.13061e9	+	2.96671e9i	0.101988	+	0.0331380i	−0.257578	+	0.966257i	$0.582925\pi$
$548$	−3.93486e9	+	1.95151e9i	−0.0436322	+	0.0216396i
$549$	−4.05677e10			−0.446571
$550$	1.99539e10	−	5.73115e10i	0.218061	−	0.626312i
$551$			8.99357e10i			0.975722i
$552$	1.16625e10	+	2.95028e10i	0.125613	+	0.317765i
$553$	−8.18196e9	+	2.51815e10i	−0.0874897	+	0.269266i
$554$	−7.30413e10	−	3.07193e10i	−0.775407	−	0.326116i
$555$	−1.33879e11	−	1.72552e11i	−1.41104	−	1.81864i
$556$	1.03158e11	−	1.51950e10i	1.07945	−	0.159001i
$557$	1.32413e11			1.37566			0.687830	−	0.725872i	$-0.258563\pi$
$557$	1.32413e11			1.37566			0.687830	+	0.725872i	$0.258563\pi$
$558$	6.68985e9	+	2.85455e10i	0.0690048	+	0.294443i
$559$	1.17099e11	−	1.61173e11i	1.19924	−	1.65061i
$560$	3.30256e10	−	2.44962e10i	0.335814	−	0.249084i
$561$	−4.17210e10	+	3.03121e10i	−0.421215	+	0.306030i
$562$	1.81788e10	−	2.10527e10i	0.182230	−	0.211039i
$563$	9.15251e10	−	1.25973e11i	0.910975	−	1.25385i	−0.0558573	−	0.998439i	$-0.517789\pi$
$563$	9.15251e10	−	1.25973e11i	0.910975	−	1.25385i	0.966833	−	0.255411i	$-0.0822108\pi$
$564$	−1.03500e11	+	5.13311e10i	−1.02288	+	0.507299i
$565$	−4.42705e10	−	3.00783e10i	−0.434431	−	0.295162i
$566$	1.07903e10	+	9.31731e9i	0.105140	+	0.0907872i
$567$	−5.04802e10	+	1.64020e10i	−0.488414	+	0.158695i
$568$	3.08786e10	+	7.94612e9i	0.296663	+	0.0763417i
$569$	2.37300e10	+	7.30335e10i	0.226386	+	0.696744i	0.998148	+	0.0608326i	$0.0193756\pi$
$569$	2.37300e10	+	7.30335e10i	0.226386	+	0.696744i	−0.771762	+	0.635911i	$0.780624\pi$
$570$	9.07172e10	+	1.39710e11i	0.859390	+	1.32352i
$571$	−3.32576e10	−	1.08061e10i	−0.312858	−	0.101654i	0.148380	−	0.988930i	$-0.452594\pi$
$571$	−3.32576e10	−	1.08061e10i	−0.312858	−	0.101654i	−0.461237	+	0.887277i	$0.652594\pi$
$572$	8.63080e10	+	4.51605e10i	0.806245	+	0.421866i
$573$	1.26973e11	−	9.22511e10i	1.17785	−	0.855762i
$574$	−4.98542e10	−	4.19544e9i	−0.459255	−	0.0386483i
$575$	2.04776e10	+	2.47409e10i	0.187330	+	0.226331i
$576$	3.39905e10	+	1.87345e10i	0.308794	+	0.170197i
$577$	−3.71397e10	+	2.69836e10i	−0.335070	+	0.243443i	−0.742579	−	0.669759i	$-0.766398\pi$
$577$	−3.71397e10	+	2.69836e10i	−0.335070	+	0.243443i	0.407509	+	0.913201i	$0.366398\pi$
$578$	−5.60022e10	−	2.35531e10i	−0.501758	−	0.211026i
$579$	−2.96672e10	−	9.63946e9i	−0.263975	−	0.0857706i
$580$	5.87210e10	+	5.63384e10i	0.518897	+	0.497843i
$581$	−1.22106e10	−	3.75804e10i	−0.107160	−	0.329804i
$582$	7.98746e10	+	6.72179e9i	0.696172	+	0.0585859i
$583$	5.35929e10	−	1.74134e10i	0.463909	−	0.150733i
$584$	2.93500e10	−	2.42536e10i	0.252323	−	0.208509i
$585$	1.91993e10	+	5.33076e10i	0.163931	+	0.455162i
$586$	−7.95368e9	−	1.31385e10i	−0.0674494	−	0.111418i
$587$	−8.10078e10	+	1.11498e11i	−0.682299	+	0.939104i	−0.999959	−	0.00910114i	$-0.997103\pi$
$587$	−8.10078e10	+	1.11498e11i	−0.682299	+	0.939104i	0.317660	+	0.948205i	$0.397103\pi$
$588$	−8.19943e10	+	8.02367e10i	−0.685921	+	0.671218i
$589$	−1.13317e11	+	8.23300e10i	−0.941533	+	0.684064i
$590$	2.25805e10	+	1.18473e9i	0.186349	+	0.00977713i
$591$	−1.45619e9	+	2.00427e9i	−0.0119362	+	0.0164288i
$592$	5.26672e9	−	2.43040e11i	0.0428798	−	1.97875i
$593$	2.40972e11			1.94871			0.974356	−	0.225010i	$-0.0722416\pi$
$593$	2.40972e11			1.94871			0.974356	+	0.225010i	$0.0722416\pi$
$594$	−6.05248e10	+	1.41844e10i	−0.486170	+	0.113937i
$595$	−3.32811e10	+	1.19865e10i	−0.265540	+	0.0956368i
$596$	−4.01921e10	+	7.68128e10i	−0.318534	+	0.608763i
$597$	−4.86758e10	+	1.49809e11i	−0.383191	+	1.17934i
$598$	−4.40995e10	+	2.66967e10i	−0.344849	+	0.208763i
$599$		−	1.17364e11i		−	0.911650i	−0.890070	−	0.455825i	$-0.849344\pi$
$599$		−	1.17364e11i		−	0.911650i	0.890070	−	0.455825i	$-0.150656\pi$
$600$	1.48048e11	+	2.82874e10i	1.14234	+	0.218267i
$601$	2.29067e10			0.175576			0.0877879	−	0.996139i	$-0.472020\pi$
$601$	2.29067e10			0.175576			0.0877879	+	0.996139i	$0.472020\pi$
$602$	−4.22869e10	−	6.98524e10i	−0.321973	−	0.531858i
$603$	6.46543e10	+	2.10074e10i	0.489022	+	0.158893i
$604$	−1.40758e11	−	7.36512e10i	−1.05761	−	0.553391i
$605$	−2.09295e10	+	7.20726e10i	−0.156220	+	0.537959i
$606$	−3.27664e10	−	1.39814e11i	−0.242962	−	1.03672i
$607$			2.00204e11i			1.47475i	0.675485	+	0.737374i	$0.263934\pi$
$607$			2.00204e11i			1.47475i	−0.675485	+	0.737374i	$0.736066\pi$
$608$	−1.95481e10	+	1.84385e11i	−0.143051	+	1.34931i
$609$	3.89122e10	+	2.82714e10i	0.282890	+	0.205531i
$610$	−1.63712e11	−	6.28542e10i	−1.18239	−	0.453957i
$611$	−1.10346e11	−	1.51878e11i	−0.791756	−	1.08976i
$612$	−2.33524e10	−	2.38640e10i	−0.166466	−	0.170113i
$613$	2.34318e10	+	1.70242e10i	0.165945	+	0.120566i	0.667658	−	0.744468i	$-0.267297\pi$
$613$	2.34318e10	+	1.70242e10i	0.165945	+	0.120566i	−0.501713	+	0.865034i	$0.667297\pi$
$614$	6.05633e10	−	3.66635e10i	0.426124	−	0.257965i
$615$	−1.12420e11	−	1.44895e11i	−0.785858	−	1.01287i
$616$	3.07767e10	−	2.54326e10i	0.213747	−	0.176631i
$617$	5.36645e10	+	1.65162e11i	0.370294	+	1.13965i	0.946599	+	0.322413i	$0.104494\pi$
$617$	5.36645e10	+	1.65162e11i	0.370294	+	1.13965i	−0.576305	+	0.817234i	$0.695506\pi$
$618$	−7.92675e9	+	9.41930e10i	−0.0543427	+	0.645750i
$619$	−1.14501e11	+	3.72035e10i	−0.779911	+	0.253408i	−0.671802	−	0.740731i	$-0.734480\pi$
$619$	−1.14501e11	+	3.72035e10i	−0.779911	+	0.253408i	−0.108109	+	0.994139i	$0.534480\pi$
$620$	−1.72304e10	+	1.25561e11i	−0.116608	+	0.849746i
$621$	1.01663e10	−	3.12886e10i	0.0683590	−	0.210387i
$622$	−4.67713e10	+	1.11208e11i	−0.312477	+	0.742978i
$623$	−2.65141e10	−	3.64936e10i	−0.176005	−	0.242250i
$624$	−7.97299e10	+	2.28421e11i	−0.525875	+	1.50660i
$625$	1.51375e11	−	1.91981e10i	0.992054	−	0.125816i
$626$	−2.24597e10	+	2.66887e11i	−0.146253	+	1.73792i
$627$	9.50706e10	+	1.30853e11i	0.615143	+	0.846671i
$628$	1.24726e11	−	2.38369e11i	0.801898	−	1.53254i
$629$	−6.46255e10	+	1.98897e11i	−0.412859	+	1.27065i
$630$	2.31913e10	+	1.21677e9i	0.147218	+	0.00772410i
$631$	−2.46690e11	+	8.01545e10i	−1.55609	+	0.505604i	−0.955760	−	0.294148i	$-0.904964\pi$
$631$	−2.46690e11	+	8.01545e10i	−1.55609	+	0.505604i	−0.600330	+	0.799753i	$0.704964\pi$
$632$	−1.04624e11	−	2.69233e10i	−0.655787	−	0.168757i
$633$	−1.98673e10	−	6.11453e10i	−0.123744	−	0.380845i
$634$	−1.29428e10	+	1.49889e10i	−0.0801071	+	0.0927711i
$635$	−1.74837e11	−	2.25342e11i	−1.07532	−	1.38595i
$636$	6.21856e10	+	1.25386e11i	0.380068	+	0.766337i
$637$	−1.50816e11	−	1.09574e11i	−0.915986	−	0.665503i
$638$	5.98043e10	+	5.16406e10i	0.360952	+	0.311680i
$639$	1.05848e10	+	1.45687e10i	0.0634860	+	0.0873809i
$640$	1.08143e11	+	1.28267e11i	0.644584	+	0.764533i
$641$	1.61845e11	+	1.17587e11i	0.958666	+	0.696512i	0.952841	−	0.303471i	$-0.0981456\pi$
$641$	1.61845e11	+	1.17587e11i	0.958666	+	0.696512i	0.00582561	+	0.999983i	$0.498146\pi$
$642$	2.37062e11	−	5.55573e10i	1.39548	−	0.327040i
$643$		−	8.39525e10i		−	0.491122i	−0.969381	−	0.245561i	$-0.921028\pi$
$643$		−	8.39525e10i		−	0.491122i	0.969381	−	0.245561i	$-0.0789722\pi$
$644$	3.07906e9	+	2.09036e10i	0.0179009	+	0.121529i
$645$	8.34717e10	−	2.87442e11i	0.482281	−	1.66078i
$646$	6.18400e10	−	1.47037e11i	0.355091	−	0.844301i
$647$	7.78021e10	+	2.52794e10i	0.443991	+	0.144261i	0.522476	−	0.852654i	$-0.325008\pi$
$647$	7.78021e10	+	2.52794e10i	0.443991	+	0.144261i	−0.0784853	+	0.996915i	$0.525008\pi$
$648$	−7.96148e10	−	2.01403e11i	−0.451537	−	1.14226i
$649$	2.19552e10			0.123754
$650$	−5.11394e9	+	2.44871e11i	−0.0286485	+	1.37178i
$651$			7.49093e10i			0.417073i
$652$	−8.62809e10	−	1.73970e11i	−0.477446	−	0.962683i
$653$	5.51775e10	−	1.69819e11i	0.303465	−	0.933970i	−0.676780	−	0.736185i	$-0.736625\pi$
$653$	5.51775e10	−	1.69819e11i	0.303465	−	0.933970i	0.980245	−	0.197785i	$-0.0633748\pi$
$654$	−7.80382e10	+	1.85552e11i	−0.426576	+	1.01427i
$655$	−2.75886e10	+	9.93631e9i	−0.149887	+	0.0539834i
$656$	4.42256e9	−	2.04085e11i	0.0238813	−	1.10204i
$657$	2.15037e10			0.115412
$658$	−7.49160e10	+	1.75571e10i	−0.399642	+	0.0936590i
$659$	1.81245e11	−	2.49462e11i	0.961000	−	1.32270i	0.0145359	−	0.999894i	$-0.495373\pi$
$659$	1.81245e11	−	2.49462e11i	0.961000	−	1.32270i	0.946464	−	0.322809i	$-0.104627\pi$
$660$	1.44992e11	+	1.98968e10i	0.764132	+	0.104860i
$661$	2.83241e11	−	2.05786e11i	1.48371	−	1.07798i	0.507376	−	0.861725i	$-0.330616\pi$
$661$	2.83241e11	−	2.05786e11i	1.48371	−	1.07798i	0.976337	−	0.216256i	$-0.0693844\pi$
$662$	1.01051e11	+	8.72572e10i	0.526151	+	0.454328i
$663$	1.22338e11	−	1.68384e11i	0.633151	−	0.871458i
$664$	1.49936e11	−	5.92699e10i	0.771319	−	0.304903i
$665$	3.75944e10	+	1.04383e11i	0.192237	+	0.533754i
$666$	8.97315e10	−	1.03917e11i	0.456087	−	0.528189i
$667$	−3.97694e10	+	1.29219e10i	−0.200931	+	0.0652863i
$668$	4.27629e10	−	2.52275e11i	0.214764	−	1.26698i
$669$	8.87353e9	+	2.73099e10i	0.0442988	+	0.136338i
$670$	2.28366e11	+	1.84949e11i	1.13327	+	0.917812i
$671$	−1.61939e11	−	5.26172e10i	−0.798844	−	0.259560i
$672$	7.36323e10	+	6.64194e10i	0.361070	+	0.325700i
$673$	1.09536e11	−	7.95826e10i	0.533945	−	0.387934i	−0.287886	−	0.957665i	$-0.592953\pi$
$673$	1.09536e11	−	7.95826e10i	0.533945	−	0.387934i	0.821831	+	0.569731i	$0.192953\pi$
$674$	−1.87456e10	+	2.22753e11i	−0.0908365	+	1.07940i
$675$	−9.96628e10	−	1.20412e11i	−0.480085	−	0.580035i
$676$	−1.81719e11	−	3.08030e10i	−0.870189	−	0.147505i
$677$	−2.24537e11	+	1.63136e11i	−1.06889	+	0.776596i	−0.975713	−	0.219053i	$-0.929703\pi$
$677$	−2.24537e11	+	1.63136e11i	−1.06889	+	0.776596i	−0.0931798	+	0.995649i	$0.529703\pi$
$678$	5.00397e10	−	1.18980e11i	0.236808	−	0.563059i
$679$	5.07737e10	+	1.64974e10i	0.238869	+	0.0776133i
$680$	−5.72654e10	−	1.32485e11i	−0.267828	−	0.619629i
$681$	5.47354e9	+	1.68458e10i	0.0254495	+	0.0783255i
$682$	−1.03195e10	+	1.22626e11i	−0.0477003	+	0.566819i
$683$	−1.29596e11	+	4.21083e10i	−0.595537	+	0.193502i	−0.591249	−	0.806489i	$-0.701365\pi$
$683$	−1.29596e11	+	4.21083e10i	−0.595537	+	0.193502i	−0.00428806	+	0.999991i	$0.501365\pi$
$684$	−7.48467e10	+	7.32423e10i	−0.341939	+	0.334609i
$685$	−8.86967e9	−	6.02624e9i	−0.0402851	−	0.0273706i
$686$	−1.44574e11	+	8.75214e10i	−0.652821	+	0.395201i
$687$	1.48248e11	−	2.04045e11i	0.665520	−	0.916009i
$688$	2.73718e11	−	1.89945e11i	1.22166	−	0.847764i
$689$	−1.83994e11	+	1.33680e11i	−0.816446	+	0.593183i
$690$	−4.87455e10	+	6.01884e10i	−0.215049	+	0.265532i
$691$	−5.64002e10	+	7.76283e10i	−0.247382	+	0.340493i	−0.914592	−	0.404377i	$-0.867488\pi$
$691$	−5.64002e10	+	7.76283e10i	−0.247382	+	0.340493i	0.667210	+	0.744870i	$0.267488\pi$
$692$	5.11869e10	+	3.47506e11i	0.223221	+	1.51544i
$693$	2.25491e10			0.0977678
$694$	−8.48093e10	−	3.61880e11i	−0.365600	−	1.56001i
$695$	1.56051e11	+	2.01129e11i	0.668848	+	0.862057i
$696$	−1.05246e11	+	1.65642e11i	−0.448504	+	0.705884i
$697$	−5.42673e10	+	1.67017e11i	−0.229936	+	0.707670i
$698$	−5.52007e10	−	9.11843e10i	−0.232553	−	0.384148i
$699$			8.10992e10i			0.339710i
$700$	9.17038e10	+	4.08421e10i	0.381940	+	0.170105i
$701$	5.83193e10			0.241513			0.120756	−	0.992682i	$-0.461468\pi$
$701$	5.83193e10			0.241513			0.120756	+	0.992682i	$0.461468\pi$
$702$	2.14629e11	−	1.29931e11i	0.883771	−	0.535013i
$703$	6.23819e11	+	2.02691e11i	2.55409	+	0.829876i
$704$	1.11385e11	+	1.18871e11i	0.453459	+	0.483935i
$705$	−2.33301e11	−	1.58510e11i	−0.944409	−	0.641652i
$706$	3.38404e11	−	7.93073e10i	1.36212	−	0.319223i
$707$		−	9.56430e10i		−	0.382803i
$708$	7.94648e9	+	5.39484e10i	0.0316258	+	0.214707i
$709$	−1.37678e11	−	1.00029e11i	−0.544853	−	0.395859i	0.281031	−	0.959699i	$-0.409324\pi$
$709$	−1.37678e11	−	1.00029e11i	−0.544853	−	0.395859i	−0.825884	+	0.563840i	$0.809324\pi$
$710$	2.01429e10	+	7.51920e10i	0.0792663	+	0.295895i
$711$	−3.58637e10	−	4.93621e10i	−0.140338	−	0.193159i
$712$	1.41877e11	−	1.17242e11i	0.552069	−	0.456207i
$713$	−5.26875e10	−	3.82797e10i	−0.203868	−	0.148119i
$714$	−4.41787e10	−	7.29775e10i	−0.169989	−	0.280799i
$715$	7.49890e9	+	2.37697e11i	0.0286928	+	0.909493i
$716$	3.72832e10	−	3.64840e10i	0.141860	−	0.138820i
$717$	−5.76166e10	−	1.77326e11i	−0.218007	−	0.670957i
$718$	−3.21753e11	−	2.70769e10i	−1.21067	−	0.101883i
$719$	3.74234e11	−	1.21596e11i	1.40032	−	0.454992i	0.491027	−	0.871145i	$-0.336622\pi$
$719$	3.74234e11	−	1.21596e11i	1.40032	−	0.454992i	0.909295	+	0.416153i	$0.136622\pi$
$720$	9.35302e8	+	9.47502e10i	0.00348034	+	0.352574i
$721$	−1.94547e10	+	5.98755e10i	−0.0719920	+	0.221569i
$722$	−2.10681e11	−	8.86069e10i	−0.775312	−	0.326076i
$723$	2.83675e11	+	3.90446e11i	1.03817	+	1.42892i
$724$	−3.83897e11	−	6.50740e10i	−1.39720	−	0.236839i
$725$	−4.93613e10	+	1.92444e11i	−0.178663	+	0.696550i
$726$	−1.80354e11	−	1.51776e10i	−0.649203	−	0.0546332i
$727$	1.95211e11	+	2.68685e11i	0.698822	+	0.961846i	0.999966	+	0.00826711i	$0.00263153\pi$
$727$	1.95211e11	+	2.68685e11i	0.698822	+	0.961846i	−0.301144	+	0.953579i	$0.597368\pi$
$728$	−8.64148e10	+	1.36005e11i	−0.307654	+	0.484205i
$729$	−3.86284e10	+	1.18886e11i	−0.136772	+	0.420940i
$730$	8.67790e10	+	3.33172e10i	0.305579	+	0.117321i
$731$	−2.72591e11	+	8.85701e10i	−0.954644	+	0.310183i
$732$	7.06787e10	−	4.16961e11i	0.246175	−	1.45228i
$733$	−1.63257e11	−	5.02455e11i	−0.565532	−	1.74053i	−0.666365	−	0.745625i	$-0.732151\pi$
$733$	−1.63257e11	−	5.02455e11i	−0.565532	−	1.74053i	0.100833	−	0.994903i	$-0.467849\pi$
$734$	1.57704e11	+	1.36176e11i	0.543324	+	0.469156i
$735$	−2.68970e11	−	7.81075e10i	−0.921626	−	0.267635i
$736$	−8.43433e10	+	1.78481e10i	−0.287435	+	0.0608247i
$737$	2.30842e11	+	1.67716e11i	0.782428	+	0.568467i
$738$	7.53492e10	−	8.72610e10i	0.254011	−	0.294168i
$739$	−7.30799e10	−	1.00586e11i	−0.245030	−	0.337255i	0.668733	−	0.743503i	$-0.266837\pi$
$739$	−7.30799e10	−	1.00586e11i	−0.245030	−	0.337255i	−0.913763	+	0.406248i	$0.866837\pi$
$740$	5.23120e11	−	2.80333e11i	1.74451	−	0.934862i
$741$	−5.28118e11	−	3.83700e11i	−1.75169	−	1.27268i
$742$	2.12697e10	+	9.07578e10i	0.0701692	+	0.299411i
$743$			1.56884e11i			0.514781i	0.966308	+	0.257390i	$0.0828626\pi$
$743$			1.56884e11i			0.514781i	−0.966308	+	0.257390i	$0.917137\pi$
$744$	−3.05051e11	+	1.90262e10i	−0.995590	+	0.0620954i
$745$	−2.11547e11	+	6.67390e9i	−0.686722	+	0.0216648i
$746$	−1.97170e11	−	8.29247e10i	−0.636629	−	0.267749i
$747$	8.66009e10	+	2.81383e10i	0.278125	+	0.0903682i
$748$	−6.22668e10	−	1.25550e11i	−0.198907	−	0.401059i
$749$	1.62168e11			0.515274
$750$	1.17436e11	+	3.48741e11i	0.371156	+	1.10220i
$751$			3.04106e11i			0.956016i	0.878355	+	0.478008i	$0.158641\pi$
$751$			3.04106e11i			0.956016i	−0.878355	+	0.478008i	$0.841359\pi$
$752$	−9.05251e10	−	3.00619e11i	−0.283073	−	0.940037i
$753$	1.29517e11	−	3.98614e11i	0.402855	−	1.23986i
$754$	−2.93959e11	−	1.23631e11i	−0.909496	−	0.382510i
$755$	−1.22298e10	−	3.87655e11i	−0.0376384	−	1.19305i
$756$	−1.49856e10	−	1.01736e11i	−0.0458760	−	0.311450i
$757$	−6.11599e11			−1.86244			−0.931221	−	0.364454i	$-0.881256\pi$
$757$	−6.11599e11			−1.86244			−0.931221	+	0.364454i	$0.881256\pi$
$758$	−6.64711e10	−	2.83632e11i	−0.201352	−	0.859168i
$759$	−4.42035e10	+	6.08409e10i	−0.133196	+	0.183328i
$760$	−4.15525e11	+	1.79607e11i	−1.24550	+	0.538354i
$761$	−2.66910e11	+	1.93921e11i	−0.795840	+	0.578212i	−0.909691	−	0.415286i	$-0.863681\pi$
$761$	−2.66910e11	+	1.93921e11i	−0.795840	+	0.578212i	0.113851	+	0.993498i	$0.463681\pi$
$762$	4.49535e11	−	5.20601e11i	1.33335	−	1.54413i
$763$	−7.88029e10	+	1.08463e11i	−0.232511	+	0.320024i
$764$	1.89501e11	+	3.82094e11i	0.556209	+	1.12149i
$765$	2.27327e10	−	7.82821e10i	0.0663752	−	0.228569i
$766$	−3.93926e11	−	3.40152e11i	−1.14419	−	0.988003i
$767$	−8.42733e10	+	2.73821e10i	−0.243505	+	0.0791197i
$768$	−2.51776e11	+	3.16720e11i	−0.723718	+	0.910398i
$769$	6.46439e10	+	1.98954e11i	0.184851	+	0.568914i	0.999946	−	0.0104144i	$-0.00331505\pi$
$769$	6.46439e10	+	1.98954e11i	0.184851	+	0.568914i	−0.815095	+	0.579328i	$0.803315\pi$
$770$	9.09975e10	+	3.49368e10i	0.258861	+	0.0993849i
$771$	−6.44651e11	−	2.09460e11i	−1.82434	−	0.592765i
$772$	3.93008e10	−	7.51093e10i	0.110645	−	0.211458i
$773$	−4.07651e11	+	2.96176e11i	−1.14175	+	0.829529i	−0.987362	−	0.158482i	$-0.949340\pi$
$773$	−4.07651e11	+	2.96176e11i	−1.14175	+	0.829529i	−0.154386	+	0.988011i	$0.549340\pi$
$774$	1.87504e11	+	1.57793e10i	0.522454	+	0.0439667i
$775$	−2.87663e11	+	1.13975e11i	−0.797401	+	0.315938i
$776$	−5.42858e10	+	2.10955e11i	−0.149706	+	0.581758i
$777$	2.83796e11	−	2.06190e11i	0.778614	−	0.565696i
$778$	−6.00325e11	−	2.52481e11i	−1.63858	−	0.689144i
$779$	5.23832e11	+	1.70203e11i	1.42247	+	0.462188i
$780$	−5.81354e11	+	1.04458e11i	−1.57059	+	0.282205i
$781$	2.33567e10	+	7.18844e10i	0.0627779	+	0.193210i
$782$	7.39047e10	+	6.21940e9i	0.197627	+	0.0166311i
$783$	1.93555e11	−	6.28897e10i	0.514940	−	0.167314i
$784$	−1.77739e11	−	2.56128e11i	−0.470455	−	0.677941i
$785$	6.56482e11	−	2.07108e10i	1.72880	−	0.0545404i
$786$	−3.66223e10	−	6.04953e10i	−0.0959523	−	0.158501i
$787$	−3.08126e11	+	4.24099e11i	−0.803211	+	1.10552i	0.189125	+	0.981953i	$0.439435\pi$
$787$	−3.08126e11	+	4.24099e11i	−0.803211	+	1.10552i	−0.992336	+	0.123572i	$0.960565\pi$
$788$	−4.70868e9	−	4.81183e9i	−0.0122122	−	0.0124797i
$789$	4.96696e10	−	3.60871e10i	0.128169	−	0.0931201i
$790$	−6.82489e10	−	2.54768e11i	−0.175221	−	0.654090i
$791$	5.05301e10	−	6.95487e10i	0.129076	−	0.177657i
$792$	5.72722e9	+	9.18259e10i	0.0145560	+	0.233380i
$793$	6.87213e11			1.73779
$794$	−1.67022e11	+	3.91429e10i	−0.420235	+	0.0984852i
$795$	−1.92028e11	+	2.82635e11i	−0.480725	+	0.707551i
$796$	−3.79275e11	−	1.98454e11i	−0.944716	−	0.494321i
$797$	6.91162e10	−	2.12718e11i	0.171296	−	0.527194i	−0.828149	−	0.560508i	$-0.810606\pi$
$797$	6.91162e10	−	2.12718e11i	0.171296	−	0.527194i	0.999445	+	0.0333137i	$0.0106060\pi$
$798$	−2.28886e11	+	1.38562e11i	−0.564427	+	0.341690i
$799$			2.70089e11i			0.662704i
$800$	−1.43028e11	+	3.83816e11i	−0.349191	+	0.937052i
$801$	1.03949e11			0.252516
$802$	−6.30346e10	−	1.04125e11i	−0.152364	−	0.251685i
$803$	8.58393e10	+	2.78909e10i	0.206454	+	0.0670811i
$804$	−3.28561e11	+	6.27927e11i	−0.786307	+	1.50274i
$805$	−4.07563e10	+	3.16217e10i	−0.0970534	+	0.0753013i
$806$	−1.13326e11	−	4.83559e11i	−0.268527	−	1.14580i
$807$			6.41194e11i			1.51180i
$808$	3.89484e11	−	2.42923e10i	0.913786	−	0.0569932i
$809$	−1.53577e11	−	1.11580e11i	−0.358535	−	0.260491i	0.393906	−	0.919151i	$-0.371124\pi$
$809$	−1.53577e11	−	1.11580e11i	−0.358535	−	0.260491i	−0.752441	+	0.658660i	$0.771124\pi$
$810$	3.32765e11	−	4.10881e11i	0.773032	−	0.954500i
$811$	1.85619e11	+	2.55482e11i	0.429080	+	0.590578i	0.967742	−	0.251944i	$-0.0810700\pi$
$811$	1.85619e11	+	2.55482e11i	0.429080	+	0.590578i	−0.538662	+	0.842522i	$0.681070\pi$
$812$	−9.34200e10	+	9.14175e10i	−0.214890	+	0.210283i
$813$	−4.08635e11	−	2.96891e11i	−0.935348	−	0.679570i
$814$	4.92976e11	−	2.98435e11i	1.12287	−	0.679755i
$815$	2.66434e11	−	3.92149e11i	0.603893	−	0.888834i
$816$	2.85963e11	−	1.98443e11i	0.644985	−	0.447585i
$817$	2.77790e11	+	8.54951e11i	0.623489	+	1.91890i
$818$	−3.71490e10	+	4.41439e11i	−0.0829724	+	0.985956i
$819$	−8.65527e10	+	2.81227e10i	−0.192373	+	0.0625059i
$820$	4.39273e11	−	2.35401e11i	0.971582	−	0.520658i
$821$	−4.37000e10	+	1.34495e11i	−0.0961854	+	0.296028i	−0.987561	−	0.157238i	$-0.949741\pi$
$821$	−4.37000e10	+	1.34495e11i	−0.0961854	+	0.296028i	0.891375	+	0.453266i	$0.149741\pi$
$822$	1.00255e10	−	2.38377e10i	0.0219594	−	0.0522129i
$823$	1.00318e11	+	1.38076e11i	0.218665	+	0.300967i	0.904231	−	0.427044i	$-0.140445\pi$
$823$	1.00318e11	+	1.38076e11i	0.218665	+	0.300967i	−0.685565	+	0.728011i	$0.740445\pi$
$824$	−2.48771e11	−	6.40172e10i	−0.539623	−	0.138863i
$825$	1.31613e11	+	3.32179e11i	0.284107	+	0.717061i
$826$	−3.04562e9	+	3.61909e10i	−0.00654267	+	0.0777461i
$827$	−3.98455e11	−	5.48427e11i	−0.851839	−	1.17246i	−0.983454	−	0.181155i	$-0.942016\pi$
$827$	−3.98455e11	−	5.48427e11i	−0.851839	−	1.17246i	0.131615	−	0.991301i	$-0.457984\pi$
$828$	−4.31415e10	−	2.25737e10i	−0.0917855	−	0.0480266i
$829$	4.78856e10	−	1.47377e11i	0.101388	−	0.312041i	−0.887478	−	0.460851i	$-0.847544\pi$
$829$	4.78856e10	−	1.47377e11i	0.101388	−	0.312041i	0.988866	+	0.148810i	$0.0475443\pi$
$830$	3.05884e11	+	2.47730e11i	0.644531	+	0.521994i
$831$	4.43700e11	−	1.44167e11i	0.930434	−	0.302316i
$832$	−5.75797e11	−	3.17361e11i	−1.20164	−	0.662308i
$833$	8.28782e10	+	2.55073e11i	0.172132	+	0.529766i
$834$	−4.01232e11	+	4.64663e11i	−0.829339	+	0.960447i
$835$	5.87734e11	−	2.11678e11i	1.20902	−	0.435442i
$836$	−3.93772e11	+	1.95293e11i	−0.806158	+	0.399817i
$837$	2.56426e11	+	1.86304e11i	0.522468	+	0.379595i
$838$	1.32117e11	+	1.14082e11i	0.267907	+	0.231335i
$839$	4.39605e11	+	6.05064e11i	0.887186	+	1.22111i	0.974378	+	0.224916i	$0.0722106\pi$
$839$	4.39605e11	+	6.05064e11i	0.887186	+	1.22111i	−0.0871920	+	0.996192i	$0.527789\pi$
$840$	−5.29110e10	+	2.36244e11i	−0.106274	+	0.474508i
$841$	1.95433e11	+	1.41990e11i	0.390672	+	0.283840i
$842$	2.09303e10	−	4.90516e9i	0.0416415	−	0.00975899i
$843$			1.63769e11i			0.324280i
$844$	1.72849e11	−	2.54603e10i	0.340642	−	0.0501758i
$845$	−1.52476e11	−	4.23357e11i	−0.299072	−	0.830387i
$846$	6.87419e10	−	1.63448e11i	0.134196	−	0.319079i
$847$	−1.14646e11	−	3.72506e10i	−0.222753	−	0.0723769i
$848$	−3.64188e11	+	1.09668e11i	−0.704275	+	0.212078i
$849$	−8.39373e10			−0.161556
$850$	2.13026e11	−	2.80689e11i	0.408092	−	0.537711i
$851$			3.04974e11i			0.581493i
$852$	−1.68180e11	+	8.34098e10i	−0.319166	+	0.158292i
$853$	−2.74643e11	+	8.45265e11i	−0.518767	+	1.59660i	0.257554	+	0.966264i	$0.417084\pi$
$853$	−2.74643e11	+	8.45265e11i	−0.518767	+	1.59660i	−0.776321	+	0.630338i	$0.782916\pi$
$854$	1.09198e11	−	2.59640e11i	0.205297	−	0.488136i
$855$	−2.45523e11	−	7.12987e10i	−0.459440	−	0.133419i
$856$	4.11889e10	+	6.60392e11i	0.0767159	+	1.23000i
$857$	−5.24907e10			−0.0973104			−0.0486552	−	0.998816i	$-0.515494\pi$
$857$	−5.24907e10			−0.0973104			−0.0486552	+	0.998816i	$0.515494\pi$
$858$	−5.58390e11	+	1.30863e11i	−1.03036	+	0.241472i
$859$	2.23321e11	−	3.07375e11i	0.410164	−	0.564542i	−0.553094	−	0.833119i	$-0.686553\pi$
$859$	2.23321e11	−	3.07375e11i	0.410164	−	0.564542i	0.963258	+	0.268576i	$0.0865531\pi$
$860$	7.32232e11	+	3.54191e11i	1.33861	+	0.647506i
$861$	2.38309e11	−	1.73141e11i	0.433638	−	0.315056i
$862$	−2.92023e11	−	2.52160e11i	−0.528918	−	0.456716i
$863$	3.46166e11	−	4.76457e11i	0.624082	−	0.858975i	−0.373561	−	0.927606i	$-0.621863\pi$
$863$	3.46166e11	−	4.76457e11i	0.624082	−	0.858975i	0.997642	+	0.0686313i	$0.0218632\pi$
$864$	4.10492e11	−	8.68652e10i	0.736630	−	0.155880i
$865$	−6.77540e11	+	5.25686e11i	−1.21024	+	0.938992i
$866$	6.50209e11	−	7.52999e11i	1.15606	−	1.33882i
$867$	3.40194e11	−	1.10536e11i	0.602074	−	0.195626i
$868$	−2.00704e11	−	3.40211e10i	−0.353571	−	0.0599336i
$869$	−7.91379e10	−	2.43561e11i	−0.138773	−	0.427100i
$870$	−4.78467e11	−	2.51036e10i	−0.835169	−	0.0438187i
$871$	−1.09524e12	−	3.55864e11i	−1.90299	−	0.618318i
$872$	−4.61705e11	−	2.93358e11i	−0.798544	−	0.507379i
$873$	−9.95294e10	+	7.23124e10i	−0.171354	+	0.124496i
$874$	1.95065e10	−	2.31794e11i	0.0334298	−	0.397243i
$875$	2.31538e10	+	2.43991e11i	0.0394994	+	0.416238i
$876$	−3.74647e10	+	2.21019e11i	−0.0636218	+	0.375330i
$877$	4.66757e11	−	3.39119e11i	0.789028	−	0.573263i	−0.118647	−	0.992937i	$-0.537856\pi$
$877$	4.66757e11	−	3.39119e11i	0.789028	−	0.573263i	0.907675	+	0.419674i	$0.137856\pi$
$878$	4.14910e11	−	9.86533e11i	0.698194	−	1.66010i
$879$	8.60003e10	+	2.79432e10i	0.144060	+	0.0468081i
$880$	−1.19160e11	+	3.79440e11i	−0.198700	+	0.632721i
$881$	−2.41037e10	−	7.41837e10i	−0.0400111	−	0.123142i	0.929056	−	0.369940i	$-0.120622\pi$
$881$	−2.41037e10	−	7.41837e10i	−0.0400111	−	0.123142i	−0.969067	+	0.246798i	$0.920622\pi$
$882$	1.47653e10	−	1.75455e11i	0.0243987	−	0.289928i
$883$	−9.03067e11	+	2.93424e11i	−1.48552	+	0.482673i	−0.935755	−	0.352650i	$-0.885281\pi$
$883$	−9.03067e11	+	2.93424e11i	−1.48552	+	0.482673i	−0.549760	+	0.835323i	$0.685281\pi$
$884$	3.95588e11	+	4.04253e11i	0.647790	+	0.661980i
$885$	−1.05184e11	+	8.16098e10i	−0.171466	+	0.133036i
$886$	8.74062e11	−	5.29135e11i	1.41843	−	0.858681i
$887$	−2.83347e11	+	3.89994e11i	−0.457746	+	0.630033i	−0.974039	−	0.226379i	$-0.927311\pi$
$887$	−2.83347e11	+	3.89994e11i	−0.457746	+	0.630033i	0.516294	+	0.856412i	$0.327311\pi$
$888$	9.11742e11	+	1.10332e12i	1.46629	+	1.77440i
$889$	3.70620e11	−	2.69272e11i	0.593366	−	0.431105i
$890$	4.19489e11	+	1.61055e11i	0.668591	+	0.256693i
$891$	3.01759e11	−	4.15335e11i	0.478794	−	0.659004i
$892$	−7.72013e10	+	1.13716e10i	−0.121945	+	0.0179623i
$893$	8.47104e11			1.33208
$894$	−1.16466e11	−	4.96958e11i	−0.182326	−	0.777983i
$895$	1.22302e11	+	3.55158e10i	0.190608	+	0.0553516i
$896$	−2.11398e11	+	1.67117e11i	−0.327996	+	0.259292i
$897$	9.37921e10	−	2.88662e11i	0.144876	−	0.445882i
$898$	−2.89572e11	−	4.78335e11i	−0.445298	−	0.735574i
$899$		−	4.02872e11i		−	0.616778i
$900$	−2.00356e11	+	1.15644e11i	−0.305374	+	0.176260i
$901$	3.27202e11			0.496497
$902$	4.13961e11	−	2.50601e11i	0.625365	−	0.378580i
$903$	4.57233e11	+	1.48564e11i	0.687680	+	0.223441i
$904$	2.96055e11	+	1.88107e11i	0.443301	+	0.281665i
$905$	−3.22119e11	−	8.94378e11i	−0.480200	−	1.33330i
$906$	9.10666e11	−	2.13421e11i	1.35159	−	0.316756i
$907$			3.52972e11i			0.521568i	0.965397	+	0.260784i	$0.0839811\pi$
$907$			3.52972e11i			0.521568i	−0.965397	+	0.260784i	$0.916019\pi$
$908$	−4.76208e10	+	7.01444e9i	−0.0700572	+	0.0103193i
$909$	1.78308e11	+	1.29549e11i	0.261166	+	0.189748i
$910$	−3.92858e11	−	2.06121e10i	−0.572889	−	0.0300577i
$911$	1.17576e11	+	1.61830e11i	0.170705	+	0.234955i	0.885795	−	0.464078i	$-0.153614\pi$
$911$	1.17576e11	+	1.61830e11i	0.170705	+	0.234955i	−0.715090	+	0.699033i	$0.753614\pi$
$912$	−6.22396e11	−	8.96892e11i	−0.899678	−	1.29647i
$913$	3.09200e11	+	2.24647e11i	0.444996	+	0.323309i
$914$	−3.07370e11	−	5.07736e11i	−0.440430	−	0.727534i
$915$	9.71410e11	−	3.49863e11i	1.38586	−	0.499129i
$916$	4.79369e11	+	4.89869e11i	0.680907	+	0.695822i
$917$	−1.45545e10	−	4.47941e10i	−0.0205835	−	0.0633496i
$918$	−3.59688e11	−	3.02693e10i	−0.506472	−	0.0426218i
$919$	−4.66750e11	+	1.51656e11i	−0.654368	+	0.212617i	−0.617339	−	0.786697i	$-0.711789\pi$
$919$	−4.66750e11	+	1.51656e11i	−0.654368	+	0.212617i	−0.0370290	+	0.999314i	$0.511789\pi$
$920$	−1.39124e11	−	1.57939e11i	−0.194201	−	0.220464i
$921$	−1.28808e11	+	3.96429e11i	−0.179021	+	0.550969i
$922$	2.83549e11	+	1.19253e11i	0.392378	+	0.165024i
$923$	−1.79305e11	−	2.46792e11i	−0.247050	−	0.340036i
$924$	−3.92859e10	+	2.31763e11i	−0.0538951	+	0.317948i
$925$	1.22360e12	+	7.76100e11i	1.67136	+	1.06011i
$926$	1.19140e12	+	1.00261e11i	1.62037	+	0.136361i
$927$	−8.52752e10	−	1.17371e11i	−0.115479	−	0.158944i
$928$	−3.96004e11	−	3.57212e11i	−0.533959	−	0.481653i
$929$	3.30230e11	−	1.01634e12i	0.443357	−	1.36451i	−0.440919	−	0.897547i	$-0.645347\pi$
$929$	3.30230e11	−	1.01634e12i	0.443357	−	1.36451i	0.884276	−	0.466965i	$-0.154653\pi$
$930$	−4.06373e11	−	6.25840e11i	−0.543241	−	0.836627i
$931$	8.00008e11	−	2.59939e11i	1.06487	−	0.345997i
$932$	−2.17289e11	−	3.68324e10i	−0.287987	−	0.0488165i
$933$	−2.19500e11	−	6.75552e11i	−0.289673	−	0.891522i
$934$	9.41666e11	+	8.13121e11i	1.23740	+	1.06848i
$935$	1.92279e11	−	2.83004e11i	0.251585	−	0.370294i
$936$	−1.36507e11	−	3.45323e11i	−0.177848	−	0.449906i
$937$	−7.32663e11	−	5.32311e11i	−0.950486	−	0.690568i	0.000435789	−	1.00000i	$-0.499861\pi$
$937$	−7.32663e11	−	5.32311e11i	−0.950486	−	0.690568i	−0.950922	+	0.309431i	$0.899861\pi$
$938$	−3.08485e11	+	3.57252e11i	−0.398494	+	0.461491i
$939$	−9.26886e11	−	1.27575e12i	−1.19224	−	1.64098i
$940$	5.30651e11	−	5.53093e11i	0.679669	−	0.708413i
$941$	−3.72200e11	−	2.70419e11i	−0.474698	−	0.344888i	0.324571	−	0.945861i	$-0.394780\pi$
$941$	−3.72200e11	−	2.70419e11i	−0.474698	−	0.344888i	−0.799269	+	0.600973i	$0.794780\pi$
$942$	3.61422e11	+	1.54219e12i	0.458999	+	1.95854i
$943$			2.56092e11i			0.323854i
$944$	−1.48153e11	−	3.21049e9i	−0.186561	−	0.00404281i
$945$	1.98357e11	−	1.53900e11i	0.248726	−	0.192980i
$946$	7.28020e11	+	3.06186e11i	0.909031	+	0.382315i
$947$	7.92284e10	+	2.57429e10i	0.0985102	+	0.0320079i	0.357857	−	0.933776i	$-0.383507\pi$
$947$	7.92284e10	+	2.57429e10i	0.0985102	+	0.0320079i	−0.259347	+	0.965784i	$0.583507\pi$
$948$	5.69835e11	−	2.82612e11i	0.705531	−	0.349911i
$949$	−3.64272e11			−0.449118
$950$	−8.80349e11	−	6.68134e11i	−1.08084	−	0.820293i
$951$		−	1.16598e11i		−	0.142551i
$952$	2.15593e11	−	8.52240e10i	0.262474	−	0.103756i
$953$	−4.17464e11	+	1.28482e12i	−0.506113	+	1.55766i	0.292778	+	0.956180i	$0.405420\pi$
$953$	−4.17464e11	+	1.28482e12i	−0.506113	+	1.55766i	−0.798891	+	0.601476i	$0.794580\pi$
$954$	−1.98011e11	−	8.32782e10i	−0.239054	−	0.100540i
$955$	−5.85177e11	+	8.61287e11i	−0.703516	+	1.03546i
$956$	5.01275e11	−	7.38367e10i	0.600129	−	0.0883977i
$957$	−4.65217e11			−0.554636
$958$	3.67566e11	+	1.56840e12i	0.436389	+	1.86207i
$959$	1.01238e10	−	1.39342e10i	0.0119693	−	0.0164743i
$960$	−9.75487e11	−	1.55465e11i	−1.14852	−	0.183040i
$961$	−1.82391e11	+	1.32515e11i	−0.213851	+	0.155372i
$962$	−1.52004e12	+	1.76035e12i	−1.77483	+	2.05541i
$963$	−2.19657e11	+	3.02332e11i	−0.255411	+	0.351543i
$964$	−1.17495e12	+	5.82723e11i	−1.36054	+	0.674768i
$965$	2.06855e11	−	6.52589e9i	0.238538	−	0.00752542i
$966$	−9.41579e10	−	8.13046e10i	−0.108130	−	0.0933698i
$967$	−4.21734e11	+	1.37030e11i	−0.482317	+	0.156714i	−0.540076	−	0.841616i	$-0.681604\pi$
$967$	−4.21734e11	+	1.37030e11i	−0.482317	+	0.156714i	0.0577592	+	0.998331i	$0.481604\pi$
$968$	1.22576e11	−	4.76329e11i	0.139606	−	0.542507i
$969$	2.90218e11	+	8.93200e11i	0.329177	+	1.01310i
$970$	−5.13693e11	+	1.37611e11i	−0.580252	+	0.155441i
$971$	9.32307e11	+	3.02925e11i	1.04877	+	0.340767i	0.782187	−	0.623044i	$-0.214104\pi$
$971$	9.32307e11	+	3.02925e11i	1.04877	+	0.340767i	0.266587	+	0.963811i	$0.414104\pi$
$972$	5.34284e11	+	2.79563e11i	0.598560	+	0.313195i
$973$	−3.30797e11	+	2.40338e11i	−0.369072	+	0.268146i
$974$	−9.44845e10	−	7.95128e9i	−0.104984	−	0.00883489i
$975$	−9.19469e11	−	1.11090e12i	−1.01746	−	1.22929i
$976$	1.08506e12	+	3.78738e11i	1.19579	+	0.417388i
$977$	8.35998e11	−	6.07388e11i	0.917544	−	0.666635i	−0.0253677	−	0.999678i	$-0.508076\pi$
$977$	8.35998e11	−	6.07388e11i	0.917544	−	0.666635i	0.942911	+	0.333044i	$0.108076\pi$
$978$	1.05392e12	+	4.43253e11i	1.15200	+	0.484502i
$979$	4.14946e11	+	1.34824e11i	0.451711	+	0.146770i
$980$	3.31430e11	−	6.85176e11i	0.359325	−	0.742844i
$981$	−9.54700e10	−	2.93826e11i	−0.103084	−	0.317260i
$982$	1.07144e11	+	9.01663e9i	0.115218	+	0.00969612i
$983$	−7.97924e11	+	2.59261e11i	−0.854570	+	0.277667i	−0.703359	−	0.710835i	$-0.748317\pi$
$983$	−7.97924e11	+	2.59261e11i	−0.854570	+	0.277667i	−0.151211	+	0.988502i	$0.548317\pi$
$984$	7.65606e11	+	9.26481e11i	0.816630	+	0.988226i
$985$	4.58373e9	−	1.57845e10i	0.00486938	−	0.0167682i
$986$	2.37599e11	+	3.92483e11i	0.251384	+	0.415253i
$987$	2.66288e11	−	3.66514e11i	0.280597	−	0.386209i
$988$	1.26790e12	−	1.24072e12i	1.33063	−	1.30210i
$989$	−3.38145e11	+	2.45677e11i	−0.353442	+	0.256791i
$990$	−1.88389e11	+	1.22326e11i	−0.196117	+	0.127344i
$991$	−5.12520e11	+	7.05423e11i	−0.531393	+	0.731400i	−0.987342	−	0.158606i	$-0.949300\pi$
$991$	−5.12520e11	+	7.05423e11i	−0.531393	+	0.731400i	0.455949	+	0.890006i	$0.349300\pi$
$992$	8.75667e10	−	8.25962e11i	0.0904257	−	0.852930i
$993$	−7.86078e11			−0.808479
$994$	−1.21734e11	+	2.85292e10i	−0.124700	+	0.0292243i
$995$	−3.29534e10	−	1.04454e12i	−0.0336208	−	1.06570i
$996$	−4.40090e11	+	8.41074e11i	−0.447202	+	0.854667i
$997$	4.70386e11	−	1.44770e12i	0.476074	−	1.46520i	−0.368431	−	0.929655i	$-0.620105\pi$
$997$	4.70386e11	−	1.44770e12i	0.476074	−	1.46520i	0.844504	−	0.535549i	$-0.179895\pi$
$998$	−8.83318e11	+	5.34739e11i	−0.890420	+	0.539038i
$999$		−	1.48428e12i		−	1.49024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.39	✓	464
4.3	odd	2	inner	100.9.j.b.11.84	yes	464
25.16	even	5	inner	100.9.j.b.91.84	yes	464
100.91	odd	10	inner	100.9.j.b.91.39	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.39	✓	464	1.1	even	1	trivial
100.9.j.b.11.84	yes	464	4.3	odd	2	inner
100.9.j.b.91.39	yes	464	100.91	odd	10	inner
100.9.j.b.91.84	yes	464	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.28596 - 13.6873i) q^{2} +(89.5931 + 29.1106i) q^{3} +(-118.686 + 226.825i) q^{4} +(-624.689 + 19.7078i) q^{5} +(-343.919 - 1467.50i) q^{6} -1003.88i q^{7} +(4088.06 - 254.974i) q^{8} +(1871.54 + 1359.75i) q^{9} +(5445.90 + 8387.03i) q^{10} +(5707.24 + 7855.34i) q^{11} +(-17236.4 + 16867.0i) q^{12} +(-31703.7 - 23034.1i) q^{13} +(-13740.4 + 8318.08i) q^{14} +(-56541.6 - 16419.4i) q^{15} +(-37363.4 - 53841.9i) q^{16} +(17422.3 + 53620.2i) q^{17} +(3103.88 - 36883.2i) q^{18} +(168174. - 54643.0i) q^{19} +(69671.5 - 144034. i) q^{20} +(29223.4 - 89940.4i) q^{21} +(60228.6 - 143206. i) q^{22} +(48326.1 + 66515.1i) q^{23} +(373684. + 96161.7i) q^{24} +(389848. - 24622.5i) q^{25} +(-52579.5 + 624799. i) q^{26} +(-235199. - 323724. i) q^{27} +(227704. + 119146. i) q^{28} +(-157167. + 483712. i) q^{29} +(243764. + 909953. i) q^{30} +(-753344. + 244776. i) q^{31} +(-427360. + 957536. i) q^{32} +(282656. + 869925. i) q^{33} +(589557. - 682759. i) q^{34} +(19784.2 + 627111. i) q^{35} +(-530551. + 263129. i) q^{36} +(3.00094e6 + 2.18031e6i) q^{37} +(-2.14140e6 - 1.84908e6i) q^{38} +(-2.16990e6 - 2.98661e6i) q^{39} +(-2.54874e6 + 239846. i) q^{40} +(2.51995e6 + 1.83085e6i) q^{41} +(-1.47319e6 + 345252. i) q^{42} +5.08373e6i q^{43} +(-2.45916e6 + 362228. i) q^{44} +(-1.19593e6 - 812539. i) q^{45} +(509986. - 1.21260e6i) q^{46} +(4.55608e6 + 1.48036e6i) q^{47} +(-1.78013e6 - 5.91153e6i) q^{48} +4.75703e6 q^{49} +(-3.56728e6 - 5.13196e6i) q^{50} +5.31117e6i q^{51} +(8.98750e6 - 4.45738e6i) q^{52} +(1.79340e6 - 5.51951e6i) q^{53} +(-2.48206e6 + 5.90161e6i) q^{54} +(-3.72006e6 - 4.79467e6i) q^{55} +(-255962. - 4.10390e6i) q^{56} +1.66579e7 q^{57} +(7.92300e6 - 1.85681e6i) q^{58} +(1.32908e6 - 1.82932e6i) q^{59} +(1.04350e7 - 1.08763e7i) q^{60} +(-1.41872e7 + 1.03076e7i) q^{61} +(9.59251e6 + 8.28306e6i) q^{62} +(1.36502e6 - 1.87879e6i) q^{63} +(1.66472e7 - 2.08469e6i) q^{64} +(2.02589e7 + 1.37643e7i) q^{65} +(9.56487e6 - 1.10770e7i) q^{66} +(2.79483e7 - 9.08096e6i) q^{67} +(-1.42302e7 - 2.41215e6i) q^{68} +(2.39339e6 + 7.36610e6i) q^{69} +(8.41954e6 - 5.46701e6i) q^{70} +(7.40334e6 + 2.40549e6i) q^{71} +(7.99766e6 + 5.08155e6i) q^{72} +(7.52022e6 - 5.46376e6i) q^{73} +(4.97696e6 - 5.91408e7i) q^{74} +(3.56445e7 + 9.14270e6i) q^{75} +(-7.56543e6 + 4.46314e7i) q^{76} +(7.88579e6 - 5.72936e6i) q^{77} +(-2.28990e7 + 5.44471e7i) q^{78} +(-2.50843e7 - 8.15037e6i) q^{79} +(2.44016e7 + 3.28981e7i) q^{80} +(-1.63387e7 - 5.02852e7i) q^{81} +(4.17924e6 - 4.96617e7i) q^{82} +(3.74353e7 - 1.21635e7i) q^{83} +(1.69323e7 + 1.73033e7i) q^{84} +(-1.19402e7 - 3.31526e7i) q^{85} +(6.95827e7 - 4.21236e7i) q^{86} +(-2.81622e7 + 3.87620e7i) q^{87} +(2.53344e7 + 3.06579e7i) q^{88} +(3.63526e7 - 2.64117e7i) q^{89} +(-1.21208e6 + 2.31017e7i) q^{90} +(-2.31234e7 + 3.18266e7i) q^{91} +(-2.08229e7 + 3.06717e6i) q^{92} -7.46200e7 q^{93} +(-1.74893e7 - 7.46267e7i) q^{94} +(-1.03979e8 + 3.74492e7i) q^{95} +(-6.61629e7 + 7.33480e7i) q^{96} +(-1.64337e7 + 5.05777e7i) q^{97} +(-3.94166e7 - 6.51111e7i) q^{98} +2.24620e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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